Question

Find the missing measurement. Round your answer to the nearest tenth.
height = 6.3 cm
top = 6.9 cm
bottom = ? cm
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 will 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 (6.9 cm),
- \( b_2 \) is the length of the bottom base (unknown),
- \( h \) is the height (6.3 cm),
- Area is given as 30.9 cm².

Plugging in the known values, we can rearrange the formula to solve for \( b_2 \):

\[
30.9 = \frac{1}{2} \times (6.9 + b_2) \times 6.3
\]

First, simplify the equation:

\[
30.9 = (6.9 + b_2) \times 3.15
\]

Now divide both sides by 3.15:

\[
\frac{30.9}{3.15} = 6.9 + b_2
\]

Calculating the left side:

\[
\frac{30.9}{3.15} \approx 9.8
\]

Now we have:

\[
9.8 = 6.9 + b_2
\]

Subtracting 6.9 from both sides gives:

\[
b_2 = 9.8 - 6.9 = 2.9
\]

So, the missing measurement for the bottom is:

\[
b_2 \approx 2.9 \, \text{cm}
\]

Thus, the answer is **2.9 cm**.