Question

trapezoid area using pythagorean theorem
6 m
find the area of the trapezoid but
first find the height
5 m
9 m
trapezoid area using pythagorean theorem
find the area of the trapezoid but
10 m
first find the height
6 m
20 m

Explanation:

---

First Trapezoid (Top)

Step1: Find base of right triangle

$9 - 6 = 3$ m

Step2: Calculate height via Pythagoras

Let $h$ = height.
$h = \sqrt{5^2 - 3^2} = \sqrt{25 - 9} = \sqrt{16} = 4$ m

Step3: Compute trapezoid area

Area formula: $\frac{1}{2} \times (a + b) \times h$, where $a=6$, $b=9$, $h=4$
$\frac{1}{2} \times (6 + 9) \times 4 = \frac{1}{2} \times 15 \times 4 = 30$ m²

---

Second Trapezoid (Bottom)

Step1: Find total base of both triangles

$20 - 10 = 10$ m

Step2: Find base of one right triangle

$\frac{10}{2} = 5$ m

Step3: Calculate height via Pythagoras

Let $h$ = height.
$h = \sqrt{6^2 - 5^2} = \sqrt{36 - 25} = \sqrt{11} \approx 3.32$ m

Step4: Compute trapezoid area

Area formula: $\frac{1}{2} \times (a + b) \times h$, where $a=10$, $b=20$, $h=\sqrt{11}$
$\frac{1}{2} \times (10 + 20) \times \sqrt{11} = 15\sqrt{11} \approx 49.75$ m²

Answer:

1. Area of the top trapezoid: $30$ m²
2. Area of the bottom trapezoid: $15\sqrt{11}$ m² (or approximately $49.75$ m²)