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Find the area of the shaded region in the following figure. Use = 3.14 and round your answer to two decimal places. 16 cm 12 cm 10 cm

Find the area of the shaded region in the following figure. Use = 3.14 and round your answer to two decimal places. 16 cm 12 cm 10 cm

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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**Educational Content: Calculating the Shaded Area** To find the area of the shaded region in the figure, follow these steps. The figure consists of a circle with a square inside it. ### Circle: - **Diameter:** Given as 16 cm. - **Radius:** Half of the diameter, so 8 cm. - **Area of the Circle:** Use the formula \(A = \pi r^2\), where \(\pi = 3.14\). \[ A = 3.14 \times (8)^2 = 3.14 \times 64 = 200.96 \, \text{cm}^2 \] ### Square: - **Side Length:** Given as 10 cm. - **Area of the Square:** Use the formula \(A = s^2\). \[ A = (10)^2 = 100 \, \text{cm}^2 \] ### Shaded Area: The shaded area is the part of the circle that is not covered by the square. - **Shaded Area Calculation:** \[ \text{Shaded Area} = \text{Area of Circle} - \text{Area of Square} \] \[ \text{Shaded Area} = 200.96 - 100 = 100.96 \, \text{cm}^2 \] Therefore, the area of the shaded region is **100.96 cm\(^2\)**, rounded to two decimal places. This calculation demonstrates how to find the difference between the area of a circle and an inscribed square.
Transcribed Image Text:**Educational Content: Calculating the Shaded Area** To find the area of the shaded region in the figure, follow these steps. The figure consists of a circle with a square inside it. ### Circle: - **Diameter:** Given as 16 cm. - **Radius:** Half of the diameter, so 8 cm. - **Area of the Circle:** Use the formula \(A = \pi r^2\), where \(\pi = 3.14\). \[ A = 3.14 \times (8)^2 = 3.14 \times 64 = 200.96 \, \text{cm}^2 \] ### Square: - **Side Length:** Given as 10 cm. - **Area of the Square:** Use the formula \(A = s^2\). \[ A = (10)^2 = 100 \, \text{cm}^2 \] ### Shaded Area: The shaded area is the part of the circle that is not covered by the square. - **Shaded Area Calculation:** \[ \text{Shaded Area} = \text{Area of Circle} - \text{Area of Square} \] \[ \text{Shaded Area} = 200.96 - 100 = 100.96 \, \text{cm}^2 \] Therefore, the area of the shaded region is **100.96 cm\(^2\)**, rounded to two decimal places. This calculation demonstrates how to find the difference between the area of a circle and an inscribed square.
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