A cross is composed of 6 congruent squares. If the distance from A to B is 10 cm, find the area of the cross.
It is number 9 on the attached paper to see the figure of the cross.
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1999 Geometry State Finals 1. The measure of each interior angle of a regular polygon is eight times that of an exterior angle of the polygon. How many sides does the polygon have? a. 20 b. 17 c. 18 d. 16 e. 19 2. A rectangle is divided into four rectangles with areas 45, 25, 15, and x. Find x. a. 23 b. 27 25 45 c. 30 d. 32 x 15 e. None of these 3. The side of a square is the same length as the altitude of an equilateral triangle. Find k if the area of the square is k times the area of the triangle. a. 2 b. 3 c. 2 2 d. 2 3 e. 3 2 4. The minute hand of a courthouse clock measures 12 feet. How far, measured in feet, does the tip of the hand travel in 25 minutes? a. 7o ft. b. 5o ft. c. 8o ft. d. 12o ft. e. 10o ft. 5. How many different chords are determined by n distinct points lying on a circle? 2 ( ) ( ) a. n n - 3 b. n n + 3 c. n - 3 2 n - n 2 d. e. n + 3 2 6. Given with the following dimensions: and . What lengths are DABC AB = 10 m BC = 21 m possible for side ? AC a. b. c. 12 m [ AC [ 30 m 11 m [ AC [ 31 m 12 m <><><><>
NCGeometryFinal99 1999 Geometry State Finals 1. The measure of each interior angle of a regular polygon is eight times that of an exterior angle of the polygon. How many sides does the polygon have? a. 20 b. 17 c. 18 d. 16 e. 19 2. A rectangle is divided into four rectangles with areas 45, 25, 15, and x. Find x. a. 23 b. 27 c. 30 d. 32 e. None of these 3. The side of a square is the same length as the altitude of an equilateral triangle. Find k if the area of the square is k times the area of the triangle. a. b. c.2 3 2 2 d. e.2 3 3 2 4. The minute hand of a courthouse clock measures 12 feet. How far, measured in feet, does the tip of the hand travel in 25 minutes? a. b. c.7o ft. 5o ft. 8o ft. d. e.12o ft. 10o ft. 5. How many different chords are determined by n distinct points lying on a circle? a. b. c.n(n − 3) n(n + 3) n2 − 3 d. e.n 2 − n 2 n 2 + 3 6. Given with the following dimensions: and . What lengths are DABC AB = 10 m BC = 21 m possible for side ?AC a. b. c.12 m [ AC [ 30 m 11 m [ AC [ 31 m 12 m < ac="">< 30="" m="" d.="" e.="" not="" enough="" information11="" m="">< ac="">< 31 m 45 x 25 15 7. is a diameter of a circle in which is a chord; b is a point on such that . if ac ad ac db ω ac how long is ?ab = 9, and bc = 16, db a. 12 b. 15 c. 11 d. 14 e. 13 8. the altitude of a pyramid with a square base is 16 cm, the area of a section parallel to the base and 10 cm from the vertex is 56.25 cm2. find the area of the base. a. 136 cm2 b. 125 cm2 c. 112.5 cm2 d. 115 cm2 e. 144 cm2 9. a cross is composed of six congruent squares as shown. if then find the area of the ab = 10, cross. a 10 5 b. 100 c. 120 d. 125 e. 12 5 10. abcd is a parallelogram; on a point e is taken so that . f is the midpoint of . ab ae = 14 ab dc cuts at p. find the ratio of to .ef bd dp bp a. 1:3 b. 1:4 c. 2:5 d. 2:3 e. none of these 11. the sides of a right triangle are 3 ft., 4 ft., and 5 ft. in length. a point is taken on the hypotenuse at a distance of 2 ft. from the vertex adjacent to the 4 ft. side. find the distance from this point to the vertex of the right angle. a. ft b. ft c. ft3 3 65 5 5 3 d. ft e. ft2 5 5 3 5 5 12. six congruent circles are drawn internally tangent to a circle of radius 12 cm, each small circle touching two other small circles. compute the radius of the small circles. a. cm b. cm c. cm2 3 5 4 d. cm e. cm3 3 3 b a 13. the number of square feet in the total surface of a right circular cylinder is equal to the number of cubic feet in its volume. if the radius of its base is five times its altitude, what is its volume? a. ft3 b. ft3 c. ft31728o5 1728o 1128o 5 d. ft3 e. ft32126o5 1528o 5 14. a rectangular box measures 4 by 5 by 2 meters. what is the length of the longest broomstick that can fit into the box? a. m b. m c. m5 2 5 3 5 d. m e. m5 2 5 3 15. two poles, p feet and q feet in length are placed x feet apart. lines are drawn from the top of each pole to the bottom of the other. the two lines will intersect at how many feet above the ground. assume the poles are perpendicular to the ground. a. b. c. pq p − q pq q − p 2pq p − q d. e. pq p + q 2pq p + q 16. the area of a circular arena is square feet. if a pole placed at the center of the arena is 872 23 37.5 feet high, approximately how many feet long is a rope which will just extend from the top of this pole to the edge of the arena? a. 64.4 ft. b. 50.4 ft. c. 49.4 ft. d. 55.6 ft. e. 41.0 ft. 17. a circle has radius r. and are diameters that are perpendicular to each other with ab cd if how long is cm = 0.2. mn y ab andng y cd, mg? a. .8r b. .4r c. .2r d. .r + .2 e. r 18. a point is the circumcenter of the triangle with vertices , and (x,y) a(−5, −1), b(3, 3) . the sum of x and y is :c(5, −5) a. b. c.− 219 − 13 9 13 9 d. e.− 913 9 13 ba d c o g m n 19. a tangent and a secant are drawn to a circle from an external point. the tangent is 14" long and the internal and external segments of the secant have the ratio of 3:1. find the length of the secant. a. 21 b. 28 c. 7 d. 30 e. 32 20. a circle of radius 4 is inscribed in an equilateral triangle. is the area inside the 3 x − oy triangle and outside the circle. find the value of . x + y a. 64 b. 60 c. 48 d. 30 e. 24 21. circle o has a diameter of cm and is equilateral. which of the following best 10 dabc approximates the area of the shaded region? a. 3.043 cm2 b. 1.932 cm2 c. 0.987 cm2 d. 2.435 cm2 e. 4.529 cm2 22. a regular hexagonal prism has a base edge 4 ft. and an altitude 5 ft. the volume of the prism is a. 120 cu. ft. b. 120 cu. ft. c. cu. ft.3 (120 + 24 3 ) d. cu. ft. e. cu. ft.(120 − 24 3 ) (24 + 120 3 ) 23. triangle abc has with m and n midpoints and . what is the ratio of ab { ac ax z bc the area of the shaded region to the area of triangle abc? a. 5 8 b. 3 8 c. 34 d. 1 2 e. 7 8 24. given two overlapping unit circles. find the area of the shaded region. a. 2o + 3 3 3 b. 2o − 3 3 3 c. 2o + 3 3 d. o + 3 3 3 e. 2o − 3 3 25. if the area of a square inscribed in a circle is 15 cm2, what is the area of the square inscribed in a semicircle of the same circle? a. 3 cm2 b. 2 cm2 c. 6 cm2 d. 4 cm2 e. 5 cm2 26. the area of a base of a prism is 24 sq. in. and the volume is 72 cu. in. if the lateral edge2 intersects the base at an angle of 45o, the length of a lateral edge is a. 6 in. b. . in. c. in.6 2 2 6 d. in. e. none of these6 27. a figure is called a rep-tile if copies of the figure fit together to form a larger similar figure. consider a right triangle with legs of lengths 1 and n, where n is a positive integer. what is the minimum number of copies of this triangle that can be fitted together to form a larger similar triangle? a b. c.2 4 3 d. e. none of these5 28. if the diagonals of a rhombus are x and y units long, find the area of the rhombus in terms of x and y. a. b. c.2xy x 2y2 2 x + y 2 d. e.xy 2 x − y 2 29. find the area of the triangle having sides of length 5, 10, and 13. a. b. c.2 14 6 14 18 14 d. e.36 14 3 14 30. three planets are aligned as shown. the diameter of the smallest planet is 3000 miles and the diameter of the planet in the middle is 8000 miles. given the other dimensions in the figure, what is the diameter of the largest planet? a. 12,500 miles b. 12,800 miles c. 15,100 miles d. 15,500 miles e. none of these 31. the sides of a triangle are 10, 10, and 12. find the radius of the circumscribed circle. a. b. 5.75 c. 64 3 d. 6.25 e. 5 3 32. the base of a triangular sheet of paper is 12 inches long. 31="" m="" 45="" x="" 25="" 15="" 7.="" is="" a="" diameter="" of="" a="" circle="" in="" which="" is="" a="" chord;="" b="" is="" a="" point="" on="" such="" that="" .="" if="" ac="" ad="" ac="" db="" ω="" ac="" how="" long="" is="" ab="9," and="" bc="16," db="" a.="" 12="" b.="" 15="" c.="" 11="" d.="" 14="" e.="" 13="" 8.="" the="" altitude="" of="" a="" pyramid="" with="" a="" square="" base="" is="" 16="" cm,="" the="" area="" of="" a="" section="" parallel="" to="" the="" base="" and="" 10="" cm="" from="" the="" vertex="" is="" 56.25="" cm2.="" find="" the="" area="" of="" the="" base.="" a.="" 136="" cm2="" b.="" 125="" cm2="" c.="" 112.5="" cm2="" d.="" 115="" cm2="" e.="" 144="" cm2="" 9.="" a="" cross="" is="" composed="" of="" six="" congruent="" squares="" as="" shown.="" if="" then="" find="" the="" area="" of="" the="" ab="10," cross.="" a="" 10="" 5="" b.="" 100="" c.="" 120="" d.="" 125="" e.="" 12="" 5="" 10.="" abcd="" is="" a="" parallelogram;="" on="" a="" point="" e="" is="" taken="" so="" that="" .="" f="" is="" the="" midpoint="" of="" .="" ab="" ae="14" ab="" dc="" cuts="" at="" p.="" find="" the="" ratio="" of="" to="" .ef="" bd="" dp="" bp="" a.="" 1:3="" b.="" 1:4="" c.="" 2:5="" d.="" 2:3="" e.="" none="" of="" these="" 11.="" the="" sides="" of="" a="" right="" triangle="" are="" 3="" ft.,="" 4="" ft.,="" and="" 5="" ft.="" in="" length.="" a="" point="" is="" taken="" on="" the="" hypotenuse="" at="" a="" distance="" of="" 2="" ft.="" from="" the="" vertex="" adjacent="" to="" the="" 4="" ft.="" side.="" find="" the="" distance="" from="" this="" point="" to="" the="" vertex="" of="" the="" right="" angle.="" a.="" ft="" b.="" ft="" c.="" ft3="" 3="" 65="" 5="" 5="" 3="" d.="" ft="" e.="" ft2="" 5="" 5="" 3="" 5="" 5="" 12.="" six="" congruent="" circles="" are="" drawn="" internally="" tangent="" to="" a="" circle="" of="" radius="" 12="" cm,="" each="" small="" circle="" touching="" two="" other="" small="" circles.="" compute="" the="" radius="" of="" the="" small="" circles.="" a.="" cm="" b.="" cm="" c.="" cm2="" 3="" 5="" 4="" d.="" cm="" e.="" cm3="" 3="" 3="" b="" a="" 13.="" the="" number="" of="" square="" feet="" in="" the="" total="" surface="" of="" a="" right="" circular="" cylinder="" is="" equal="" to="" the="" number="" of="" cubic="" feet="" in="" its="" volume.="" if="" the="" radius="" of="" its="" base="" is="" five="" times="" its="" altitude,="" what="" is="" its="" volume?="" a.="" ft3="" b.="" ft3="" c.="" ft31728o5="" 1728o="" 1128o="" 5="" d.="" ft3="" e.="" ft32126o5="" 1528o="" 5="" 14.="" a="" rectangular="" box="" measures="" 4="" by="" 5="" by="" 2="" meters.="" what="" is="" the="" length="" of="" the="" longest="" broomstick="" that="" can="" fit="" into="" the="" box?="" a.="" m="" b.="" m="" c.="" m5="" 2="" 5="" 3="" 5="" d.="" m="" e.="" m5="" 2="" 5="" 3="" 15.="" two="" poles,="" p="" feet="" and="" q="" feet="" in="" length="" are="" placed="" x="" feet="" apart.="" lines="" are="" drawn="" from="" the="" top="" of="" each="" pole="" to="" the="" bottom="" of="" the="" other.="" the="" two="" lines="" will="" intersect="" at="" how="" many="" feet="" above="" the="" ground.="" assume="" the="" poles="" are="" perpendicular="" to="" the="" ground.="" a.="" b.="" c.="" pq="" p="" −="" q="" pq="" q="" −="" p="" 2pq="" p="" −="" q="" d.="" e.="" pq="" p="" +="" q="" 2pq="" p="" +="" q="" 16.="" the="" area="" of="" a="" circular="" arena="" is="" square="" feet.="" if="" a="" pole="" placed="" at="" the="" center="" of="" the="" arena="" is="" 872="" 23="" 37.5="" feet="" high,="" approximately="" how="" many="" feet="" long="" is="" a="" rope="" which="" will="" just="" extend="" from="" the="" top="" of="" this="" pole="" to="" the="" edge="" of="" the="" arena?="" a.="" 64.4="" ft.="" b.="" 50.4="" ft.="" c.="" 49.4="" ft.="" d.="" 55.6="" ft.="" e.="" 41.0="" ft.="" 17.="" a="" circle="" has="" radius="" r.="" and="" are="" diameters="" that="" are="" perpendicular="" to="" each="" other="" with="" ab="" cd="" if="" how="" long="" is="" cm="0.2." mn="" y="" ab="" andng="" y="" cd,="" mg?="" a.="" .8r="" b.="" .4r="" c.="" .2r="" d.="" .r="" +="" .2="" e.="" r="" 18.="" a="" point="" is="" the="" circumcenter="" of="" the="" triangle="" with="" vertices="" ,="" and="" (x,y)="" a(−5,="" −1),="" b(3,="" 3)="" .="" the="" sum="" of="" x="" and="" y="" is="" :c(5,="" −5)="" a.="" b.="" c.−="" 219="" −="" 13="" 9="" 13="" 9="" d.="" e.−="" 913="" 9="" 13="" ba="" d="" c="" o="" g="" m="" n="" 19.="" a="" tangent="" and="" a="" secant="" are="" drawn="" to="" a="" circle="" from="" an="" external="" point.="" the="" tangent="" is="" 14"="" long="" and="" the="" internal="" and="" external="" segments="" of="" the="" secant="" have="" the="" ratio="" of="" 3:1.="" find="" the="" length="" of="" the="" secant.="" a.="" 21="" b.="" 28="" c.="" 7="" d.="" 30="" e.="" 32="" 20.="" a="" circle="" of="" radius="" 4="" is="" inscribed="" in="" an="" equilateral="" triangle.="" is="" the="" area="" inside="" the="" 3="" x="" −="" oy="" triangle="" and="" outside="" the="" circle.="" find="" the="" value="" of="" .="" x="" +="" y="" a.="" 64="" b.="" 60="" c.="" 48="" d.="" 30="" e.="" 24="" 21.="" circle="" o="" has="" a="" diameter="" of="" cm="" and="" is="" equilateral.="" which="" of="" the="" following="" best="" 10="" dabc="" approximates="" the="" area="" of="" the="" shaded="" region?="" a.="" 3.043="" cm2="" b.="" 1.932="" cm2="" c.="" 0.987="" cm2="" d.="" 2.435="" cm2="" e.="" 4.529="" cm2="" 22.="" a="" regular="" hexagonal="" prism="" has="" a="" base="" edge="" 4="" ft.="" and="" an="" altitude="" 5="" ft.="" the="" volume="" of="" the="" prism="" is="" a.="" 120="" cu.="" ft.="" b.="" 120="" cu.="" ft.="" c.="" cu.="" ft.3="" (120="" +="" 24="" 3="" )="" d.="" cu.="" ft.="" e.="" cu.="" ft.(120="" −="" 24="" 3="" )="" (24="" +="" 120="" 3="" )="" 23.="" triangle="" abc="" has="" with="" m="" and="" n="" midpoints="" and="" .="" what="" is="" the="" ratio="" of="" ab="" {="" ac="" ax="" z="" bc="" the="" area="" of="" the="" shaded="" region="" to="" the="" area="" of="" triangle="" abc?="" a.="" 5="" 8="" b.="" 3="" 8="" c.="" 34="" d.="" 1="" 2="" e.="" 7="" 8="" 24.="" given="" two="" overlapping="" unit="" circles.="" find="" the="" area="" of="" the="" shaded="" region.="" a.="" 2o="" +="" 3="" 3="" 3="" b.="" 2o="" −="" 3="" 3="" 3="" c.="" 2o="" +="" 3="" 3="" d.="" o="" +="" 3="" 3="" 3="" e.="" 2o="" −="" 3="" 3="" 25.="" if="" the="" area="" of="" a="" square="" inscribed="" in="" a="" circle="" is="" 15="" cm2,="" what="" is="" the="" area="" of="" the="" square="" inscribed="" in="" a="" semicircle="" of="" the="" same="" circle?="" a.="" 3="" cm2="" b.="" 2="" cm2="" c.="" 6="" cm2="" d.="" 4="" cm2="" e.="" 5="" cm2="" 26.="" the="" area="" of="" a="" base="" of="" a="" prism="" is="" 24="" sq.="" in.="" and="" the="" volume="" is="" 72="" cu.="" in.="" if="" the="" lateral="" edge2="" intersects="" the="" base="" at="" an="" angle="" of="" 45o,="" the="" length="" of="" a="" lateral="" edge="" is="" a.="" 6="" in.="" b.="" .="" in.="" c.="" in.6="" 2="" 2="" 6="" d.="" in.="" e.="" none="" of="" these6="" 27.="" a="" figure="" is="" called="" a="" rep-tile="" if="" copies="" of="" the="" figure="" fit="" together="" to="" form="" a="" larger="" similar="" figure.="" consider="" a="" right="" triangle="" with="" legs="" of="" lengths="" 1="" and="" n,="" where="" n="" is="" a="" positive="" integer.="" what="" is="" the="" minimum="" number="" of="" copies="" of="" this="" triangle="" that="" can="" be="" fitted="" together="" to="" form="" a="" larger="" similar="" triangle?="" a="" b.="" c.2="" 4="" 3="" d.="" e.="" none="" of="" these5="" 28.="" if="" the="" diagonals="" of="" a="" rhombus="" are="" x="" and="" y="" units="" long,="" find="" the="" area="" of="" the="" rhombus="" in="" terms="" of="" x="" and="" y.="" a.="" b.="" c.2xy="" x="" 2y2="" 2="" x="" +="" y="" 2="" d.="" e.xy="" 2="" x="" −="" y="" 2="" 29.="" find="" the="" area="" of="" the="" triangle="" having="" sides="" of="" length="" 5,="" 10,="" and="" 13.="" a.="" b.="" c.2="" 14="" 6="" 14="" 18="" 14="" d.="" e.36="" 14="" 3="" 14="" 30.="" three="" planets="" are="" aligned="" as="" shown.="" the="" diameter="" of="" the="" smallest="" planet="" is="" 3000="" miles="" and="" the="" diameter="" of="" the="" planet="" in="" the="" middle="" is="" 8000="" miles.="" given="" the="" other="" dimensions="" in="" the="" figure,="" what="" is="" the="" diameter="" of="" the="" largest="" planet?="" a.="" 12,500="" miles="" b.="" 12,800="" miles="" c.="" 15,100="" miles="" d.="" 15,500="" miles="" e.="" none="" of="" these="" 31.="" the="" sides="" of="" a="" triangle="" are="" 10,="" 10,="" and="" 12.="" find="" the="" radius="" of="" the="" circumscribed="" circle.="" a.="" b.="" 5.75="" c.="" 64="" 3="" d.="" 6.25="" e.="" 5="" 3="" 32.="" the="" base="" of="" a="" triangular="" sheet="" of="" paper="" is="" 12="" inches="">