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5. Write a formula for the perimeter of the figure from problem #4 in terms of a, b, c, and d.

5. Write a formula for the perimeter of the figure from problem #4 in terms of a, b, c, and d.

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter10: Measurement, Area, And Volume
Section10.2: Polygons And Quadrilaterals
Problem 1E
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**Task 5: Perimeter Formula Calculation** **Objective:** Write a formula for the perimeter of the figure from problem #4 in terms of \( a, b, c, \) and \( d \). **Diagram Description:** The figure is composed of a rectangle with a semicircle on top. The rectangle has the following measurements: - Height: \( a \) - Base: \( b \) The semicircle sits on top of the rectangle, sharing its width. - The radius of the semicircle (half of the base of the rectangle): \( \frac{b}{2} \) A diagonal line extends from the top corner of the rectangle to the edge of the semicircle, labeled \( d \). **To find the perimeter:** 1. **Rectangle:** - One side of length \( a \) - One base of length \( b \) 2. **Semicircle:** - Perimeter: \( \pi \times \frac{b}{2} \) (half of the circle's circumference) 3. **Diagonal Line:** Length \( d \) Thus, the perimeter \( P \) can be formulated as: \[ P = b + 2a + \pi \times \frac{b}{2} - b + d \] \[ P = 2a + \left(\frac{\pi b}{2}\right) + d \]
Transcribed Image Text:**Task 5: Perimeter Formula Calculation** **Objective:** Write a formula for the perimeter of the figure from problem #4 in terms of \( a, b, c, \) and \( d \). **Diagram Description:** The figure is composed of a rectangle with a semicircle on top. The rectangle has the following measurements: - Height: \( a \) - Base: \( b \) The semicircle sits on top of the rectangle, sharing its width. - The radius of the semicircle (half of the base of the rectangle): \( \frac{b}{2} \) A diagonal line extends from the top corner of the rectangle to the edge of the semicircle, labeled \( d \). **To find the perimeter:** 1. **Rectangle:** - One side of length \( a \) - One base of length \( b \) 2. **Semicircle:** - Perimeter: \( \pi \times \frac{b}{2} \) (half of the circle's circumference) 3. **Diagonal Line:** Length \( d \) Thus, the perimeter \( P \) can be formulated as: \[ P = b + 2a + \pi \times \frac{b}{2} - b + d \] \[ P = 2a + \left(\frac{\pi b}{2}\right) + d \]
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