The area of a trapezoid could be determined using
[tex]\boxed{a= \frac{1}{2} \times \text{sum of base} \times \text{height} }[/tex]
The height of the trapezoid is unkown. Therefore we should determine the height first using pythagorean theorem. Look into the triangle formed on the trapezoid. The base of the triangle is 16 units. See image attached.
The height of the triangle is the same as the height of the trapezoid.
In pythagorean theorem, if you add up the square of the perpendicular lines, it results the square of the hypotenuse.
h² + 16² = (4√41)²
h² + 256 = (4²)(√41)²
h² + 256 = 16 × 41
h² + 256 = 656
h² = 656 - 256
h² = 400
h = √400
h = 20
The height of the triangle is 20 units, therefore the height of the trapezoid is also 20 units.
Find the area of the trapezoid.
[tex]a= \frac{1}{2} \times \text{sum of base} \times \text{height}[/tex]
[tex]a= \frac{1}{2} \times (16+32) \times 20[/tex]
[tex]a= \frac{1}{2} \times 48 \times 20[/tex]
a = 24 × 20
a = 480
The area of the trapezoid is 480 units²
