AnswersECASD - Geometry A - CRArea of Composite Figures

Area of Composite Figures Answers

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A rectangular pool has side lengths of 12 yards and 6 yards. An octagon is drawn around the pool. The octagon has 2 sides with lengths 12 yards, and 6 sides with lengths 6 yards. The area between the rectangle and the octagon is shaded.

Question illustration
A
176 square yards
B
196 square yards
C
208 square yards
D
280 square yards
2
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A square is inscribed in an equilateral triangle that is inscribed in a circle.

Question illustration
A
area of the circle – area of the square – area of the triangle
B
area of the triangle – area of the square + area of the circle
C
area of the triangle + area of the square + area of the circle
D
area of the circle – area of the triangle + area of the square
3

A carpenter is making a wooden window frame that has a width of 1 inch.

Question illustration
A
5.5 + 106 square inches
Option A
B
5.5 + 116 square inches
Option B
C
5.5 + 153 square inches
Option C
D
5.5 + 162 square inches
Option D
4

A composite figure is comprised of a semicircle, trapezoid, and 2 rectangles.

Question illustration
A
as a circle, three rectangles, and a triangle
B
as a circle, a trapezoid, and four triangles
C
as a semicircle, three rectangles, and a square
D
as a semicircle, a trapezoid, and two rectangles
5

3 semicircles are connected to 3 sides of a square. Each side of the square measures 4 centimeters.

Question illustration
A
(6π + 4) cm2
B
(6π + 16) cm2
C
(12π + 4) cm2
D
(12π + 16) cm2
6

A circle is inscribed in a regular hexagon with side length 10 feet. What is the area of the shaded region?

Question illustration
A
(150 – 75π) ft2
Option A
B
(300 – 75π) ft2
C
(150 – 25π) ft2
Option C
D
(300 – 25π) ft2
7

A composite figure is comprised of a square and 4 semicircles.

Question illustration
A
as a pentagon and four semicircles
B
as two rectangles and four circles
C
as a square and four semicircles
D
as two triangles and four circles
8

A square is inscribed in a circle of diameter 12 millimeters. What is the area of the shaded region?

Question illustration
A
(72π – 144) mm2
B
(72π – 72) mm2
C
(288π – 288) mm2
D
(288π – 144) mm2
9

A semicircle with a diameter of 8 meters is shown. A smaller semicircle with a diameter of 4 meters is cut out of the larger semicircle. A rectangle with side lengths of 2 meters and 5 meters is connected to the semicircle.

Question illustration
A
(6π + 10) m2
B
(10π + 10) m2
C
(12π + 10) m2
D
(16π + 10) m2
10

A trapezoid has base lengths of 12 centimeters and 13 centimeters. The other sides have lengths of 5 centimeters and 10 centimeters. A rectangle with side lengths of 2 centimeters and 5 centimeters is connected to the side with length 10 centimeters.

Question illustration
A
70 cm2
B
100 cm2
C
105 cm2
D
130 cm2

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