Question

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

Answer 1

Let's analyze the composite figure you've described step by step to find the height of the larger rectangle.

1. Start at the base of 8 cm, which indicates the width of the larger rectangle.
2. Move straight up on the right side—this gives us the height of the larger rectangle, which we will denote as \( h \).
3. Move straight left 2 cm. This action indicates that there is a 2 cm section at the top of the larger rectangle.
4. Move up 3 cm—this action gives us the height of the extension above the larger rectangle.
5. Move 4 cm across the top—this section is the top horizontal length of the shape before going down.
6. Finally, move down 3 cm to complete the shape.

Now let’s see how the height of the larger rectangle relates to the area of the composite figure:

To find the area of the larger rectangle:
- The area is given as \( 52 \) square meters.
- The width of the rectangle is \( 8 \) cm, equivalent to \( 0.8 \) meters (since \( 100 \) cm = \( 1 \) meter).

The area \( A \) of the rectangle is given by the formula:
\[
A = \text{base} \times \text{height}
\]
Substituting the known values:
\[
52 = 0.8 \times h
\]

Now solve for \( h \):
\[
h = \frac{52}{0.8}
\]
\[
h = 65
\]

Thus, the height of the larger rectangle is \( 65 \) meters.