https://file.aiquickdraw.com/mathbot/file/17274829033264xub8obw.jpg

The problem asks for the area of a composite figure, which is made up of a rectangle and two right triangles. Here's how we can solve it:

### Step-by-Step Solution:

1. **Area of the rectangle**:
   - The dimensions of the rectangle are given as \( 27 \, \text{ft} \times 11 \, \text{ft} \).
   - The area \( A_{\text{rect}} \) is calculated by multiplying the base by the height:
     \[
     A_{\text{rect}} = 27 \, \text{ft} \times 11 \, \text{ft} = 297 \, \text{square feet}
     \]

2. **Area of the two right triangles**:
   - Each triangle has a base of \( 7 \, \text{ft} \) and a height of \( 13 \, \text{ft} - 11 \, \text{ft} = 2 \, \text{ft} \).
   - The area of one triangle \( A_{\text{tri}} \) is:
     \[
     A_{\text{tri}} = \frac{1}{2} \times 7 \, \text{ft} \times 2 \, \text{ft} = 7 \, \text{square feet}
     \]
   - Since there are two triangles, the total area of the triangles is:
     \[
     A_{\text{total triangles}} = 2 \times 7 \, \text{square feet} = 14 \, \text{square feet}
     \]

3. **Total area of the composite figure**:
   - Now, add the areas of the rectangle and the two triangles:
     \[
     A_{\text{total}} = 297 \, \text{square feet} + 14 \, \text{square feet} = 311 \, \text{square feet}
     \]

### Final Answer:
The area of the composite figure is \( 311 \, \text{square feet} \).

Would you like more details or have any questions?

Here are some related questions you might find helpful:
1. How do you calculate the area of irregular shapes?
2. What is the formula for the area of a trapezoid?
3. How do you break down composite figures into simpler shapes?
4. How do you determine the height of a right triangle in composite shapes?
5. How would the area change if the dimensions of the rectangle were different?

**Tip:** Always ensure the units of measurement are consistent when calculating areas or perimeters.

Find the area of the following composite figure: A trapezoid made up of a rectangle and two right triangles, with dimensions 27 ft (rectangle base), 11 ft (rectangle height), 7 ft (triangle base), and 13 ft (triangle height).

This page provides a step-by-step solution to calculate the area of a composite figure made up of a rectangle and two right triangles. The rectangle has dimensions of 27 ft by 11 ft, and each triangle has a base of 7 ft and height of 2 ft. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation