Mathematics: The area of an isosceles trapezoid is 72m2 and its diagonals are perpendicular. find the length of a diagonal.

The area of an isosceles trapezoid is 72m2 and its

Ответ:

lala1196

04.01.2022

Mathematics

12 meters.

Step-by-step explanation:

Let h represent the length of each diagonal of the given isosceles trapezoid.

We have been given that the area of an isosceles trapezoid is $72\text{ m}^2$ and its diagonals are perpendicular.

We know that area of a trapezoid with perpendicular diagonals is equal to half the product of diagonals. $\text{Area of trapezoid}=\frac{h_1\times h_2}{2}$ , where,

$h_1\text{ and } h_2$ represents diagonals of trapezoid.

Since both diagonals of isosceles trapezoid are congruent, so our formula would be:

$\text{Area of trapezoid}=\frac{h\times h}{2}$

$72\text{ m}^2=\frac{h^2}{2}$

$2*72\text{ m}^2=\frac{h^2}{2}*2$

$144\text{ m}^2=h^2$

Upon taking square root of both sides of our equation we will get,

$\sqrt{144\text{ m}^2}=h$

$12\text{ m}=h$

Therefore, the length of each diagonal of our given trapezoid is 12 meters.

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The area of an isosceles trapezoid is 72m2 and its diagonals are perpendicular. find the length of a diagonal.

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