Question

The area on the composite figure is 52 square meters. What is the value in meters of the height of the larger rectangle?
8m is the base, straight up on right side (?) Then to the left 2 m ,up 3 m across the top 4 m ,then dow 3 m

Answer 1

To find the height of the larger rectangle in the composite figure, we need to clearly visualize and calculate the area based on the given dimensions and configuration.

1. **Base of the larger rectangle**: The base is given as **8 m**.

2. **Configuration Description**:
- You start with an 8 m base.
- Go straight up on the right side, which we need to denote as the height **h** (the height we want to find).
- Move to the left **2 m**.
- Then go up **3 m**.
- Across the top move **4 m** (this appears to not connect directly back to the original height line since we go up after moving to the left).
- Finally, go down **3 m**.

3. **Visualizing the shape**: It seems like this is a sort of composite shape where part of it might be a rectangle and part an additional vertical extension.

From your description, we can calculate the area of the composite figure using the provided dimensions. The entire area is stated to be **52 square meters**.

### Finding height (h):

Let’s break this down mathematically:
1. **Area of the larger rectangle**:
- Area = base × height
- Area = \( 8 \, \text{m} \times h \)

2. **Total area of the composite figure** includes the area of all possibly other shapes described. However, you mentioned that the area is directly given as 52 square meters.

So, we can write the equation:
\[
8h = 52
\]

3. **Solving for h**:
\[
h = \frac{52}{8} = 6.5 \, \text{meters}
\]

Thus, the height of the larger rectangle is **6.5 meters**.