### Geometry Problem: Finding the Area of Composite Shapes**Problem Statement:****15. Which houses have an area of exactly 82 square inches? Select all that apply.**Below are four different composite shapes represented as houses (A, B, C, and D). Each house is made up of basic geometric shapes such as rectangles or triangles. The dimensions for each component of the houses are provided. Determine which of the houses have a total area of exactly 82 square inches.#### House A:- Consists of a rectangle at the bottom and a triangular section on top. - **Bottom rectangle dimensions:** - Width: 9 inches - Height: 6 inches- **Top triangular section dimensions:** - The base is divided into 3 inches and 2 inches, with the height being 5 inches.**Area Calculation:**- Rectangle: $ 9 \text{ in} \times 6 \text{ in} = 54 \text{ square inches} $- Triangle: $ \frac{1}{2} \times (3 + 2) \text{ in} \times 5 \text{ in} = \frac{1}{2} \times 5 \text{ in} \times 5 \text{ in} = 12.5 \text{ square inches} $- **Total area for House A:** $ 54 + 12.5 = 66.5 \text{ square inches} $#### House B:- Consists of a rectangle with a trapezoid on top.- **Bottom rectangle dimensions:** - Width: 11 inches - Height: 8 inches- **Top trapezoid dimensions:** - Top base: 7 inches - Bottom base: 11 inches - Height: 3 inches**Area Calculation:**- Rectangle: $ 11 \text{ in} \times 8 \text{ in} = 88 \text{ square inches} $- Trapezoid: $ \frac{1}{2} \times (7 \text{ in} + 11 \text{ in}) \times 3 \text{ in} = \frac{1}{2} \times 18 \text{ in} \times 3 \text{ in} = 27 \text{ square inches} $-

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Description: ### Geometry Problem: Finding the Area of Composite Shapes**Problem Statement:****15. Which houses have an area of exactly 82 square inches? Select all that apply.**Below are four different composite shapes represented as houses (A, B, C, and D). Ea

We use Area of rectangle = Length X height Area of trapezium = (1/2)(sum of parallel…

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15. Which houses have an area of exactly 82 square inches? Select all that apply. 5 in 3 in zin 15 in A. 6 in 9 in 7 in 3 in В. 8 in 11 in 10 in C. 6 in 12 in 11 in D. 7 in 13in 6 in 10 in raft

Elementary Geometry For College Students, 7e

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Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

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### Geometry Problem: Finding the Area of Composite Shapes

**Problem Statement:**

**15. Which houses have an area of exactly 82 square inches? Select all that apply.**

Below are four different composite shapes represented as houses (A, B, C, and D). Each house is made up of basic geometric shapes such as rectangles or triangles. The dimensions for each component of the houses are provided. Determine which of the houses have a total area of exactly 82 square inches.

#### House A:

- Consists of a rectangle at the bottom and a triangular section on top.
- **Bottom rectangle dimensions:**
- Width: 9 inches
- Height: 6 inches
- **Top triangular section dimensions:**
- The base is divided into 3 inches and 2 inches, with the height being 5 inches.

**Area Calculation:**
- Rectangle: $ 9 \text{ in} \times 6 \text{ in} = 54 \text{ square inches} $
- Triangle: $ \frac{1}{2} \times (3 + 2) \text{ in} \times 5 \text{ in} = \frac{1}{2} \times 5 \text{ in} \times 5 \text{ in} = 12.5 \text{ square inches} $
- **Total area for House A:** $ 54 + 12.5 = 66.5 \text{ square inches} $

#### House B:

- Consists of a rectangle with a trapezoid on top.
- **Bottom rectangle dimensions:**
- Width: 11 inches
- Height: 8 inches
- **Top trapezoid dimensions:**
- Top base: 7 inches
- Bottom base: 11 inches
- Height: 3 inches

**Area Calculation:**
- Rectangle: $ 11 \text{ in} \times 8 \text{ in} = 88 \text{ square inches} $
- Trapezoid: $ \frac{1}{2} \times (7 \text{ in} + 11 \text{ in}) \times 3 \text{ in} = \frac{1}{2} \times 18 \text{ in} \times 3 \text{ in} = 27 \text{ square inches} $
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