Ch. 11 Worksheet #3 Honors Geometry

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1 Ch. 11 Worksheet #3 1) Find the area of the trapezoid. 2) Find the area (BC) C 12 2 B 4 3) Given: rea (BCE) = 78 sq. units, Find the length of C E 135 C B 4) Given: Parallelogram BC; M, N are midpoints. rea (BC) = 120 sq. feet. Find the area of. N C M B

2 Ch. 11 Worksheet #4 1) Find the area of BC. 2) Given: rea of Figure = rea of an equilateral with side = x = 5 C x 0 B ) rea () = 2 rea () 4) rea of Rectangle = 48 sq. in rea = rea () = 8 5) rea () = 4 rea () = 7 rea () =

3 Ch. 11 Worksheet #5 1) Given: rea Square BC = 12 sq. in E & F Trisect G rea EF= E F B G C 2) rea of Figure = ) Find area of given figure in terms of a, b, & c. c a b

4 4) Given: semi-circle with a radius R rea of semi-circle rea of square 5) rea of BE = 1 sq. units B rea of BCE = C E ) Given: BC is a parallelogram M, N are midpoints P, Q are trisection points rea BC = 24 rea (MPNQ) = M C P Q N B

5 Ch. 11 Worksheet # 1) rea () = 12 2) Find rea of Shaded Region rea () = ) Given Square CB and circle. 4) Given is the center of arc, B = 3 rea of Shaded Region = Find rea of Shaded Region. C 5 3 B B

6 Ch. 11 Worksheet #7 1) Given: C-median, CB-diameter 2) Find rea of Shaded Region B = C-radius of circle Shaded rea = 5 C 3 B 0 0 3) Find rea of Shaded Region 4) rea () rea () ) regular hexagon and a square have perimeters in the ratio of 3 to 2. (H to Sq.) Find the Ratio of reas

7 Ch. 11 Worksheet #8 1) 2) B 5 x 3 x x C rea = 42 rea = rea of BC = 180 sq. in rea = rea = rea = 3) R, RC are radii 4) B = C = BC = 8 Find the area of the shaded region. Find total area = O C R B C 5) Radius = rea of BC = 0 B C 120

8 Ch. 11 Worksheet #9 1) 8 Find the ratio of the areas of the inscribed and circumscribed circles ) rea = 8 3) O is the center of the circle. Find the area of the shaded region O

9 Ch. 11 Worksheet #10 1) 2) square and an equilateral triangle have L equal perimeters. Find the ratio of their areas. E B Z Square ELZ has an area of 25 B has an area of 200 m B = 90, = x Find LB (in terms of x) = Ratio of areas 3) 45 4) N a c L T B 27 Find the area in terms of a, b and c rea of NTL 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.. The area of one n-gon is 4 25 times that of a similar n-gon. Find the ratio of the perimeters of the two n-gons.. 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.

10 8. Point E, L and V are the midpoints of the sides of NT. What is the ratio of the area of ELV to the area of NT? The shortest side of a polygon of area 19 sq. cm. is 4 cm. long. Find the area of a similar polygon whose shortest side is 8 cm. long The sides of a quadrilateral are 3 in., 4 in., 5 in., and in. long. Find the lengths of the sides of a similar quadrilateral whose area is 9 times as great 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 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 Given: a circle with r =. Find the ratio of the areas of its inscribed and circumscribed equilateral triangles 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 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? One of two similar polygons has an area 25% more than the other. What is the ratio of the perimeters? 1.

11 Ch. 11 Worksheet #11 1) n equilateral triangle and a regular hexagon ( ) 2) Find ( ) have equal perimeters. Find the ratio of the areas ) 2) 3) 4) 4 5 3) ( ) ( ) 9 Given: 1 hexagon is inscribed to the circle, the other is circumscribed = 4) a) Find the ratio of the hexagons b) f the sum of the areas of the 2 hexagons is 3 5, find the radius of the circle. r = 5) 2 similar triangles have areas 100 and 25. ) The larger triangle has a side of 4. T R a) Find the corresponding side of the small triangle: M b) Find an altitude of the smaller triangle TRM 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?

12 7) f 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) f 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 to the area of triangle B if the base of triangle is feet long and the base of triangle B is 45 inches long and the two triangles have equal heights? 12) parallelogram has sides measuring 8 and 11 and has an included angle of 45. n equilateral triangle has a perimeter of 24. What is the ratio of the area of the parallelogram to the area of the triangle? nswers: 1. 3:2 7. ncreases by 17% 2. 1:10 8. ecreases by.25% 3. 4:9 9. ecrease by 1 2/3% 4. a. 4:3 b ncreases by 300% 5. a. 2 b :5. 2: : 4 3

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