https://file.aiquickdraw.com/mathbot/file/1728205714278e2xtes75.jpg

The shape you have uploaded is a composite geometric figure. To find its area, we need to break it down into simpler shapes like rectangles and triangles. Here's the step-by-step breakdown:

### Step 1: Split the shape
- The shape consists of:
  1. A **large rectangle** with dimensions \( 4.3 \, \text{mm} \times 9.1 \, \text{mm} \)
  2. A **right triangle** with a base of \( 8 \, \text{mm} \) and height of \( 2 \, \text{mm} \)

### Step 2: Calculate the area of the large rectangle
The formula for the area of a rectangle is:
\[
\text{Area}_{\text{rectangle}} = \text{length} \times \text{width}
\]
For the rectangle:
\[
\text{Area}_{\text{rectangle}} = 4.3 \, \text{mm} \times 9.1 \, \text{mm} = 39.13 \, \text{mm}^2
\]

### Step 3: Calculate the area of the right triangle
The formula for the area of a triangle is:
\[
\text{Area}_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height}
\]
For the triangle:
\[
\text{Area}_{\text{triangle}} = \frac{1}{2} \times 8 \, \text{mm} \times 2 \, \text{mm} = 8 \, \text{mm}^2
\]

### Step 4: Add the areas
Now, sum the areas of the rectangle and the triangle:
\[
\text{Total Area} = 39.13 \, \text{mm}^2 + 8 \, \text{mm}^2 = 47.13 \, \text{mm}^2
\]

### Final Answer:
The area of the shape is **47.13 mm²**.

Would you like a more detailed breakdown of any step, or do you have any questions?

Here are five related questions you can explore:
1. How do you find the perimeter of this composite shape?
2. What happens if the base of the triangle changes—how would that affect the area?
3. How would you calculate the area if one of the dimensions were missing?
4. How does the concept of decomposition help in solving complex area problems?
5. What other types of composite shapes can you break down using basic geometric shapes?

**Tip:** When dealing with composite shapes, always break them down into familiar simple shapes like triangles and rectangles for easier calculations.

Find the area of the composite shape consisting of a rectangle and a right triangle.

Learn how to calculate the area of a composite shape made of a rectangle and a right triangle. This problem involves basic geometric concepts and is 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