Question

What is the area of the trapezoid with height 13 units?



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units2

A rectangle with a length of 15 and a height of 13 has two triangles on each side of it with short leg lengths of 7.

Answer 1

To find the area of the trapezoid, we first need to determine the lengths of the two bases of the trapezoid.

1. **Calculate the length of the rectangle:**
The rectangle has a length of 15 units.

2. **Calculate the length of each triangle's base:**
Each triangle has a short leg length of 7 units. If we consider this as the height of the triangles, then the bases of the triangles will be equal to this leg length.

3. **Find the bases of the trapezoid:**
The left side triangle will contribute to the length of the trapezoid's base on the left, and the right side triangle will do the same on the right. Therefore, we can calculate the bases of the trapezoid:

- The length of the left base (the base of the left triangle) will be: \( 7 \) units (triangle height).
- The length of the right base (the rectangle's base plus the triangle height) will be: \( 15 + 7 = 22 \) units.

4. **Calculate the area of the trapezoid:**
The formula for the area of a trapezoid is given by:

\[
\text{Area} = \frac{1}{2} \times (b_1 + b_2) \times h
\]

where \( b_1 \) and \( b_2 \) are the lengths of the two bases, and \( h \) is the height.

Using the lengths we found:
- \( b_1 = 7 \) units
- \( b_2 = 22 \) units
- \( h = 13 \) units

Plugging these values into the formula:

\[
\text{Area} = \frac{1}{2} \times (7 + 22) \times 13
\]

\[
= \frac{1}{2} \times 29 \times 13
\]

\[
= \frac{1}{2} \times 377
\]

\[
= 188.5
\]

So the area of the trapezoid is:

\[
\boxed{188.5} \text{ units}^2
\]