Question

determine (a) the area and (b) the perimeter of the quadrilateral. note that the figure is not drawn to scale.

a. the area of the quadrilateral is 720 \\(\text{in}^2\\)

Explanation:

Convert the height to inches

Using the Unit Conversion knowledge point

$$ h = 2\text{ ft} \times 12\text{ in/ft} = 24\text{ in} $$

Find the missing base segments

Using the Pythagorean Theorem knowledge point

$$
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Since the trapezoid is isosceles (both legs are \(25\text{ in}\)), the bottom base \(b_2\) is:

$$ b_2 = 6 + 2 \times 7 = 20\text{ in} $$

Calculate the area of the trapezoid

Using the Area of Trapezoid knowledge point

$$ A = \frac{1}{2} \times (b_1 + b_2) \times h = \frac{1}{2} \times (6 + 20) \times 24 = 13 \times 24 = 312\text{ in}^2 $$

Calculate the perimeter of the trapezoid

Using the Perimeter of Trapezoid knowledge point

$$ P = b_1 + b_2 + \text{leg}_1 + \text{leg}_2 = 6 + 20 + 25 + 25 = 76\text{ in} $$

Answer:

Question 1

a. The area of the quadrilateral is <blank>\(312\)</blank> \(\text{in}^2\).

Question 2

b. The perimeter of the quadrilateral is <blank>\(76\)</blank> \(\text{in}\).