Geometry Area Worksheets Answers

Ch. 11 Worksheet #3 Honors Geometry Name: ____________________ Hour: _______ 1) Find the area of the trapezoid. ________ 2) Find the area (ABCD). _______________ 6 D C  6 30  8 12 A 2 B 4 3) Given: Area (ABCDE) = 78 sq. units, Find the length of CD_________________ D E C 135 5 2 5 2 A B 4) Given: Parallelogram ABCD; M, N are midpoints. Area (ABCD) = 120 sq. feet. Find the area of I. _________________ D N C I A M B Ch. 11 Worksheet #4 Honors Geometry Name: ____________________ Hour: _______ 1) Find the area of ABCD. _________ 2) Given: Area of Figure = Area of an equilateral ∆ with side = 2 11 . x =________ D 5 C x 45  60  A 2 3 B 7.5 3) Area (II) = 2 Area (I) Area III = _______ 4) Area of Rectangle = 48 sq. in Area (I) = _________ 6 8 II I I 6 III 5) Area (I) = 4 Area (II) = 7 Area (III) = ______ I III II Ch. 11 Worksheet #5 Honors Geometry 1) Given: Area Square ABCD = 12 sq. in E & F Trisect AG Area ∆DEF= ____________ Name: ____________________ Hour: _______ A D E F B 2) G C 10 Area of Figure = __________ 10 3 60 3 3 4 3) Find area of given figure in terms of a, b, & c. a c b 4) Given: semi-circle with a radius R Area of semi-circle – Area of square 5) Area of ∆BED = 16 sq. units B Area of ABCDE = ______ A C 45  60  E 6) Given: ABCD is a parallelogram M, N are midpoints P, Q are trisection points Area ABCD = 24 Area (MPNQ) = __________ D M C Q P A N B 60  45 D Ch. 11 Worksheet #6 Honors Geometry Name: ____________________ Hour: _______ 1) Area (I) = 12 Area (II) = _________ 2) Find Area of Shaded Region ___________ 8 4 II 8 3 8 I 8 3) Given Square DCBA and circle A. Area of Shaded Region = __________ D 4) Given A is the center of arc, AB = 3 Find Area of Shaded Region. __________ 5 C 3 6 A B A B Ch. 11 Worksheet #7 Honors Geometry Name: ____________________ Hour: _______ 1) Given: CD-median, CB-diameter BD = CD-radius of circle D Shaded Area = _________ 2) Find Area of Shaded Region ___________ 6 6 D 5 36  C 6 B 60 3) Find Area of Shaded Region 4) Area (I) – ____________ Area (II) 2 150  2 I 6 II 5) A regular hexagon and a square have perimeters in the ratio of 3 to 2. (H to Sq.) Find the Ratio of Areas ______________ 60 Ch. 11 Worksheet #8 Honors Geometry Name: ____________________ Hour: _______ 1) 2) B 5 I x I 3 II x II III x A Area I = 42 Area II = ____________ C Area of ABC = 180 sq. in Area I = ________ Area II = _________ Area III = __________ 3) DR, RC are radii Find the area of the shaded region. 4) AB = AC = BC = 8 Find total area = _________ A D 8 O C B 120  C R 5) Radius = 6 Area of ABCD = _____________ 60  A B 90 90 D C 120  Ch. 11 Worksheet #9 Honors Geometry 1) Name: ____________________ Hour: _______ 8 Find the ratio of the areas of the inscribed and circumscribed circles. 8 8 8 2) Area I = ____________ 6 I 8 3) O is the center of the circle. Find the area of the shaded region 6 6 O 6 Ch. 11 Worksheet #10 Honors Geometry Name: ____________________ Hour: _______ 1) 2) A square and an equilateral triangle have equal perimeters. Find the ratio of their areas. L E B A Z I Square ELIZ has an area of 256  IBA has an area of 200 m AIB = 90, AI = x Find LB (in terms of x) = _________ 3) Ratio of areas _________________ 4) 45 a N c A 12 2 45 120 T L B 27 Find the area in terms of a, b and c ______________ Area of NATL __________________ 5. Two regular pentagons have areas of 50 and 100 sq. inches. Find the ratio of the lengths of a pair of corresponding sides. 5.______________ 6. The area of one n-gon is the two n-gons. 25 times that of a similar n-gon. Find the ratio of the perimeters of 4 6. ______________ 7. One side of a triangle is 15 in. long and the area is 90 sq. in. Find the area of a similar triangle in which the corresponding side is 9 in. long. 7. ______________ 8. Point E, L and V are the midpoints of the sides of NAT . What is the ratio of the area of ELV to the area of NAT ? 8. ______________ 9. The shortest side of a polygon of area 196 sq. cm. is 4 cm. long. Find the area of a similar polygon whose shortest side is 8 cm. long. 9. ______________ 10. The sides of a quadrilateral are 3 in., 4 in., 5 in., and 6 in. long. Find the lengths of the sides of a similar quadrilateral whose area is 9 times as great. 10. _____________ 11. Two similar polygons have corresponding sides with lengths in the ratio 2:3. The sum of the areas of the polygons is 143 sq. in. Find the area of each. 11. _____________ 12. The shortest side of two similar polygons have lengths of 5 ft. and 12 ft. Find the length of the shortest side of a similar polygon whose area equals the sum of the areas of the two given polygons. 12. _____________ 13. Given: a circle with r = 6. Find the ratio of the areas of its inscribed and circumscribed equilateral triangles. 13. _____________ 14. Two regular hexagons have apothems in the ratio 2:3. The difference of the areas of the hexagons is 245 sq. in. Find the area of each hexagon. 14. _____________ 15. One regular hexagon is inscribed in, and another is circumscribed about, a circle with radius k. What is the ratio of the areas of the hexagon? 15. _____________ 16. One of two similar polygons has an area 25% more than the other. What is the ratio of the perimeters? 16. _____________ Ch. 11 Worksheet #11 Honors Geometry Name: ____________________ Hour: _______ 1) An equilateral triangle and a regular hexagon 2) Find A( I ) A( II ) have equal perimeters. Find the ratio of the areas. 3 5 I 13 4 13 II 10 1) _______________ 2) __________________ 3) 4) 4 5 I 6 II 9 3) A( I ) = A( II ) Given: 1 hexagon is inscribed to the circle, the other is circumscribed ____________________ 4) a) Find the ratio of the hexagons ____________ b) If the sum of the areas of the 2 hexagons is 56 3 , find the radius of the circle. r = _________ 5) 2 similar triangles have areas 100 and 25. The larger triangle has a side of 4. a) Find the corresponding side of the small triangle: __________ 6) T R M A b) Find an altitude of the smaller triangle __________ TRAM is a square inscribed in a semicircle with radius r. How does its area compare with that of a square inscribed in the whole circle? ________________________ 7) If you increase the length of the base of a rectangle by 30% and decrease the height by 10%, what happens to the area of the rectangle? 8) What happens to the area of a rectangle if you decrease the length of the base by 25% and increase the height by 25%? 9) If you increase the height of a rectangle by 20%, how would you need to change the base of the rectangle in order to keep the same area? 10) By what percent would you need to increase the height of a rectangle in order to triple the area if you are decreasing the length of the base by 25%? 11) What is the ratio of the area of triangle A to the area of triangle B if the base of triangle A is 6 feet long and the base of triangle B is 45 inches long and the two triangles have equal heights? 12) A parallelogram has sides measuring 8 and 11 and has an included angle of 45 . An equilateral triangle has a perimeter of 24. What is the ratio of the area of the parallelogram to the area of the triangle? Answers: 1. 3:2 2. 1:10 3. 4:9 4. a. 4:3 b. 4 5. a. 2 b. 25 6. 2:5 7. Increases by 17% 8. Decreases by 6.25% 9. Decrease by 16 2/3% 10. Increases by 300% 11. 8:5 12. 11 2 : 4 3