Question

Find the missing measurement. Round your answer to the nearest tenth.
top 6.9 cm
Middle 6.3 cm
bottom ?
Area= 30.9 cm^2


Question 11 options:

3 cm


2.9 cm


2.8 cm


2.3 cm

Answer 1

To find the missing measurement (the bottom), we can use the formula for the area of a trapezoid since we have two parallel sides (the top and bottom measurements) and the height (the middle measurement). The area of a trapezoid is given by the formula:

\[
\text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}
\]

In this case:
- Base₁ (top) = 6.9 cm
- Base₂ (bottom) = unknown (let's call it \( b \))
- Height (middle) = 6.3 cm
- Area = 30.9 cm²

Plugging in the values into the area formula:

\[
30.9 = \frac{1}{2} \times (6.9 + b) \times 6.3
\]

First, multiply both sides of the equation by 2 to eliminate the \(\frac{1}{2}\):

\[
61.8 = (6.9 + b) \times 6.3
\]

Next, divide both sides by 6.3:

\[
\frac{61.8}{6.3} = 6.9 + b
\]

Calculating the left side:

\[
9.8 = 6.9 + b
\]

Now, solve for \( b \):

\[
b = 9.8 - 6.9 = 2.9
\]

Thus, the missing measurement (bottom) is:

**2.9 cm**

So the answer from the options provided is:

**2.9 cm**