An isosceles trapezoid has bases of 4 and 12. If the base angle is 45°, find the area.

Solution:

Given bases of a trapezoid are 4, 12 and the base angle is 45°

Let a, b be the bases of the trapezoid and h be the height.

We know that the general formula for the area of the trapezoid is

A = (a + b) × h/2 and the formula for the height is h = (b - a)/2.

finding the area of the trapezoid with the bases and the base angle given

Here, a = 4, b = 12

Height = b - a /2 = 12 - 4 /2 = 8/2 = 4

Area = {(4 + 10) × 4} /2

Area = {14 × 4 }/2

Area = 56/2 = 28

Area of the isosceles trapezoid is 28 sq.units

An isosceles trapezoid has bases of 4 and 12. If the base angle is 45°, find the area.

Summary:

An isosceles trapezoid has bases of 4 and 10. If the base angle is 45°, its area is 28 sq.units

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