Question

Cindy wants to secure sequins on a piece of felt shaped like a trapezoid with a height of 9cm and bases of 20cm and 14cm. What is the cost of all the sequins if sequins cost $0.60 per cm2 of coverage?

Answer 1

To find the cost of all the sequins that Cindy wants to secure on the felt trapezoid, we first need to calculate the area of the trapezoid.

The area \( A \) of a trapezoid can be calculated using the formula:

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

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

Given:
- \( b_1 = 20 \, \text{cm} \)
- \( b_2 = 14 \, \text{cm} \)
- \( h = 9 \, \text{cm} \)

Plugging in these values:

\[
A = \frac{1}{2} \times (20 + 14) \times 9
\]

Calculating the sum of the bases:

\[
20 + 14 = 34
\]

Now substituting back into the area formula:

\[
A = \frac{1}{2} \times 34 \times 9
\]
\[
A = 17 \times 9
\]
\[
A = 153 \, \text{cm}^2
\]

Next, we find the cost of the sequins. The cost is given as \$0.60 per cm²:

\[
\text{Cost} = \text{Area} \times \text{Cost per cm}^2 = 153 \, \text{cm}^2 \times 0.60 \, \text{dollars/cm}^2
\]

Calculating the total cost:

\[
\text{Cost} = 153 \times 0.60 = 91.8 \, \text{dollars}
\]

Thus, the total cost of all the sequins is:

\[
\boxed{91.80 \text{ dollars}}
\]