The exact area of the isosceles trapezoid inscribed in a circle is determined as 196 sq units.
Height of the trapezoid
The height of the trapezoid is calculated as follows;
From the image, the sum of h1 and h2 is the height of the trapezoid.
Each of the height will be calculated using Pythagoras theorem as follows;
- half of b1 = 12/2 = 6
- half of b2 = 16/2 = 8
h1² = r² - (b1/2)²
h1² = 10² - 6²
h1² = 64
h1 = √64
h1 = 8
h2² = r² - (b1/2)²
h2² = 10² - 8²
h2² = 36
h2 = √36
h2 = 6
Total height = 8 + 6 = 14
Area of the trapezoid
A = ¹/₂(b₁ + b₂)H
A = ¹/₂(12 + 16) x 14
A = 196 sq units.
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