3. A trapezoid with bases that measure 5 centimeters and 7 centimeters has a height of 4.5 centimeters. What is the area of the trapezoid?

Question

UpStudy AI · Accepted Answer

The area $$ A $$ of a trapezoid is given by the formula

$$
A = \frac{1}{2} (b_1 + b_2) h,
$$

where $$ b_1 $$ and $$ b_2 $$ are the lengths of the two bases, and $$ h $$ is the height.

Given:
- $$ b_1 = 5 $$ centimeters,
- $$ b_2 = 7 $$ centimeters,
- $$ h = 4.5 $$ centimeters,

we substitute these values into the formula:

$$
A = \frac{1}{2} (5 + 7) \times 4.5.
$$

Simplify inside the parentheses:

$$
5 + 7 = 12.
$$

Now, substitute back into the formula:

$$
A = \frac{1}{2} \times 12 \times 4.5.
$$

Multiply the factors:

$$
\frac{1}{2} \times 12 = 6,
$$

so

$$
A = 6 \times 4.5.
$$

Finally, calculate the product:

$$
A = 27.
$$

Thus, the area of the trapezoid is $$ \boxed{27 \text{ cm}^2} $$.
The area of the trapezoid is 27 square centimeters.

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