https://file.aiquickdraw.com/mathbot/file/17288719456688qxm7af6.jpg

To solve for the area of this figure, we can break it down into simpler geometric shapes: a rectangle and a triangle.

1. **The Rectangle:**
   - The base is 48 m, and the height is 10 m.
   - The area of a rectangle is given by: 
     \[
     \text{Area of rectangle} = \text{base} \times \text{height}
     \]
     \[
     = 48 \, \text{m} \times 10 \, \text{m} = 480 \, \text{m}^2
     \]

2. **The Triangle:**
   - The base of the triangle is 48 m (the same as the rectangle's base), but this triangle is composed of two smaller right triangles. Each smaller right triangle has:
     - Base of 25 m.
     - Height of 17 m - 10 m = 7 m (this is because the total height from the base to the top is 17 m, and we subtract the 10 m height of the rectangle part).

   - The area of one right triangle is:
     \[
     \text{Area of one triangle} = \frac{1}{2} \times \text{base} \times \text{height}
     \]
     \[
     = \frac{1}{2} \times 25 \, \text{m} \times 7 \, \text{m} = 87.5 \, \text{m}^2
     \]

   - Since there are two such triangles:
     \[
     \text{Total area of triangles} = 2 \times 87.5 \, \text{m}^2 = 175 \, \text{m}^2
     \]

3. **Total Area:**
   - Adding the areas of the rectangle and the triangles:
     \[
     \text{Total Area} = 480 \, \text{m}^2 + 175 \, \text{m}^2 = 655 \, \text{m}^2
     \]

Thus, the area of the figure is **655 square meters**.

Would you like more details or have any questions about this? 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 right triangle?
3. How do you decompose complex figures into simpler shapes?
4. Why is the height of the triangle calculated as \( 17 \, \text{m} - 10 \, \text{m} \)?
5. What other methods can be used to find the area of composite figures?

**Tip:** When solving geometry problems, always look for ways to break complex shapes into simpler, well-known geometric figures like rectangles and triangles.

Learn how to find the area of a composite figure consisting of a rectangle and two right triangles. This problem involves calculating the area of each shape separately and adding them together. 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