Question

A trapezoid is decomposed into a recntangle and two right triangles, the top is 6 centimeters long, the bottom is 10 centimeters long, and the height of both triangles is 6 centimeters long, what’s the area

Answer 1

To find the area of the trapezoid, we can use the formula for the area of a trapezoid:

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

where:
- \( b_1 \) is the length of the top base,
- \( b_2 \) is the length of the bottom base,
- \( h \) is the height of the trapezoid.

In this case, we have:
- \( b_1 = 6 \) cm (top base),
- \( b_2 = 10 \) cm (bottom base),
- \( h = 6 \) cm (height).

Now, we can substitute these values into the formula:

\[
\text{Area} = \frac{1}{2} \times (6 + 10) \times 6
\]

Calculating the sum of the bases:

\[
6 + 10 = 16
\]

Now substituting this back into the area formula:

\[
\text{Area} = \frac{1}{2} \times 16 \times 6
\]

Calculating further:

\[
\text{Area} = 8 \times 6 = 48
\]

Thus, the area of the trapezoid is \( 48 \) square centimeters.