**4) Find the area of the composite shape.**The image shows a composite shape plotted on a Cartesian coordinate grid. The axes are labeled $x$ and $y$ with the origin point labeled $O$. The shape is composed of a combination of linear and curved segments, specifically:- It consists of a rectangle, a triangle, and half a circle.**Points and Segments:**- Point $O$ is at the origin.- Point $A$ is located 6 units up the $y$ axis from the origin.- Point $B$ is located 6 units to the right and 2 units up along the $x$ and $y$ axes respectively from the origin.- Point $C$ is located 6 units to the right along the $x$ axis and is on the same horizontal line as with $B$.- Point $D$ is located 4 units down from the origin on the negative $y$ axis.- Point $E$ is joined to point $D$ in a curved manner, forming the semicircle end of the shape, and is horizontally in line with $C$.- Point $F$ is located 4 units up on the $y$ axis from the point of intersection of the semicircle and forms a right angle triangle with points $A$ and $C$.**Steps to find the area:**1. **Rectangle Calculation**: - Identify the length and width of the rectangle. - The rectangle is made by the points $O, C, F, E$. Using the coordinate grid, the length of the rectangle along the $x$-axis is 6 units, and the height along the $y$-axis is 4 units. - Area = Length × Width = 6 units × 4 units = 24 square units.2. **Right Triangle Calculation**: - Identify the base and height of the right triangle $\triangle ACB$. - Using the coordinate grid, the base is 6 units along the $x$ axis, and the height is 4 units along the $y$ axis. - Area = $\frac{1}{2} \times Base \times Height$ = \(\frac{1}{2} \times 6 \text{ units} \times

Let's consider distance inside each grid be 1 unit. We can see that this composite shape ABCDEF…

Answered: 4) Find the area of the composite…

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4) Find the area of the composite shape. y4 |A E |B

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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Question

**4) Find the area of the composite shape.**

The image shows a composite shape plotted on a Cartesian coordinate grid. The axes are labeled $x$ and $y$ with the origin point labeled $O$. The shape is composed of a combination of linear and curved segments, specifically:

- It consists of a rectangle, a triangle, and half a circle.

**Points and Segments:**

- Point $O$ is at the origin.
- Point $A$ is located 6 units up the $y$ axis from the origin.
- Point $B$ is located 6 units to the right and 2 units up along the $x$ and $y$ axes respectively from the origin.
- Point $C$ is located 6 units to the right along the $x$ axis and is on the same horizontal line as with $B$.
- Point $D$ is located 4 units down from the origin on the negative $y$ axis.
- Point $E$ is joined to point $D$ in a curved manner, forming the semicircle end of the shape, and is horizontally in line with $C$.
- Point $F$ is located 4 units up on the $y$ axis from the point of intersection of the semicircle and forms a right angle triangle with points $A$ and $C$.

**Steps to find the area:**

1. **Rectangle Calculation**:
- Identify the length and width of the rectangle.
- The rectangle is made by the points $O, C, F, E$. Using the coordinate grid, the length of the rectangle along the $x$-axis is 6 units, and the height along the $y$-axis is 4 units.
- Area = Length × Width = 6 units × 4 units = 24 square units.

2. **Right Triangle Calculation**:
- Identify the base and height of the right triangle $\triangle ACB$.
- Using the coordinate grid, the base is 6 units along the $x$ axis, and the height is 4 units along the $y$ axis.
- Area = $\frac{1}{2} \times Base \times Height$ = \(\frac{1}{2} \times 6 \text{ units} \times

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