Question

Diagonals of an isosceles trapezoid are perpendicular to each other and the sum of the lengths of its bases is 2a. What is its area?

Answer 1

Answer:

Given:-

• sum of length of its base is 2a

Constraction:-

• Draw a figure with the shorter base on top.
• You will have 4 right triangles, 2 of which are isosceles right triangles, namely a larger one on the bottom and a smaller one on top.
• Remember that in an isosceles right triangle the ratio of the hypotenuse to the leg is √2

To find:-

• Area of isosceles trapezoid

Find:-

Let x be the length of the shorter base; the longer base is 2a - x.

The bottom triangle has legs = (2a-x)/√2 and altitude (2a - x)/2

The top triangle has legs x/√2 and altitude x/2

The altitude of the trapezoid is [(2a-x)/2] + x/2 = a

The area of the trapezoid is (1/2) * 2a * a = a2

Hence the area will be a^2❤

Answer 2

Answer:

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