Question

What is the area of a triangle for one of the legs being 3in and the hypotenuse being 9in

Answer 1

The area of a triangle for one of the legs being 3 inches and the hypotenuse being 9 inches is 12.727 square inches

Solution:

Given that to find area of a triangle for one of the legs being 3 inches and the hypotenuse being 9 inches

From given information,

Let "c" = hypotenuse = 9 inches

Let "a" = length of one of the leg of triangle = 3 inches

To find: area of triangle

The area of triangle when hypotenuse and length of one side of triangle is given:

`A = (1)/(2) a √(c^2 - a^2)`

Where, "c" is the length of hypotenuse

"a" is the length of one side of triangle

Substituting the given values we get,

`A = (1)/(2) * 3 * √(9^2 - 3^2)`

`A =(1)/(2) * 3 * √(81-9)\\\\A =(1)/(2) * 3 * √(72)\\\\A =(1)/(2) * 3 * 8.48528\\\\A = (1)/(2) * 25.45584\\\\A = 12.727`

Thus area of triangle is 12.727 square inches