Question

The lengths of the sides of a right triangle are a and b, and the hypotenuse is c. Find the area of the triangle.

b = 2 in.; c = 6 in.
A = sq. in.

Answer 1

5.7 in^2

Explanation:

First find missing leg measurement a

a^2= c^2- b^2

a^2= 36-4

a^2= 32

a= 5.7

find area of triangle

a= AB/2

a= (2*5.7)/2

a= 5.7 in^2

Answer 2

For this case we have that by definition, the area of a traingule is given by:

`A = \frac {1} {2} b * h`

Where:

b: It's the base

h: It's the height

So, in this case we have:

`b = 2 \ in`

By the Pythagorean theorem, we find the height h:

`h = \sqrt {c ^ 2-b ^ 2}\\h = \sqrt {6 ^ 2-2 ^ 2}\\h = \sqrt {36-4}\\h = \sqrt {32}\\h = \sqrt {2 ^ 5}\\h = 4 \sqrt {2} \ in`

So:

`A = \frac {1} {2} 2 * 4 \sqrt {2}\\A = 4\sqrt {2} \ in ^ 2`

Answer:

`4 \sqrt {2} \ in ^ 2`