https://file.aiquickdraw.com/mathbot/file/172920152949871wxxtzs.jpg

To solve for the area of the figure, we need to find the areas of the rectangle and the triangle separately and then sum them.

### Step 1: Area of the rectangle
The area \( A \) of a rectangle is given by the formula:
\[
A = \text{base} \times \text{height}
\]
- Base = 18 inches
- Height = 15 inches

So,
\[
A_{\text{rectangle}} = 18 \times 15 = 270 \, \text{in}^2
\]

### Step 2: Area of the triangle
The area \( A \) of a triangle is given by:
\[
A = \frac{1}{2} \times \text{base} \times \text{height}
\]
- Base = 12 inches
- Height = 9 inches

So,
\[
A_{\text{triangle}} = \frac{1}{2} \times 12 \times 9 = 54 \, \text{in}^2
\]

### Step 3: Total area of the figure
To find the total area, add the area of the rectangle and the area of the triangle:
\[
A_{\text{total}} = A_{\text{rectangle}} + A_{\text{triangle}} = 270 + 54 = 324 \, \text{in}^2
\]

Thus, the area of the figure is **324 square inches**.

Would you like further details or have any questions?

### Related Questions:
1. How would the area change if the height of the triangle was doubled?
2. How do you calculate the perimeter of this figure?
3. What if the entire shape was a parallelogram, how would the area change?
4. How can we calculate the area of a circle inscribed inside the triangle?
5. How do you find the area of irregular shapes?

**Tip:** Always label the dimensions carefully and double-check units when calculating areas.

Find the area of the figure consisting of a rectangle and a triangle, given dimensions: rectangle with base 18 inches and height 15 inches, and triangle with base 12 inches and height 9 inches.

Learn how to calculate the total area of a composite figure consisting of a rectangle and a triangle. The rectangle has dimensions of 18 inches by 15 inches, and the triangle has a base of 12 inches and a height of 9 inches. Follow step-by-step to solve this problem for 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