Question

3.) eileen admires a beautiful stained-glass window in a museum. the window and its dimensions are shown in the diagram below.how many square feet of glass were used to create the window? use 3.14 for π.

Explanation:

Step1: Calculate trapezoid area

The trapezoid has bases $b_1=12\ \text{ft}$, $b_2=12+8+8=28\ \text{ft}$, height $h=18\ \text{ft}$.
Area formula: $\frac{1}{2}(b_1+b_2)h$
$\frac{1}{2}(12+28)\times18 = \frac{1}{2}\times40\times18 = 360\ \text{sq ft}$

Step2: Calculate semicircle area

The semicircle has diameter $12\ \text{ft}$, so radius $r=\frac{12}{2}=6\ \text{ft}$.
Area formula: $\frac{1}{2}\pi r^2$
$\frac{1}{2}\times3.14\times6^2 = \frac{1}{2}\times3.14\times36 = 56.52\ \text{sq ft}$

Step3: Sum the two areas

Add trapezoid and semicircle areas.
$360 + 56.52 = 416.52$

Answer:

$416.52$ square feet