The lengths of the sides of a triangle are 5 m, 5 m and 8 m. What is…

The correct answer is Option 1: $12 m^2$

Step 1: Calculate the semi-perimeter (s)

s= (5+5+8)/2 =9m

Step 2: Use Heron's formula for area (A): √s(s-a)(s-b)(s-c)

A = √9 (9-5)(9-5)(9-8)

     =√9*4*4

     =√144 = $12 m^2$

Alternatively, We can find the area of the triangle by finding the height of the triangle. 

Using the Pythagorean theorem: $hypotenuse^2$ = $base^2$  + $height^2$

$5^2$ = $4^2$ + $height^2$

$height^2$ =25 - 16 = 9

Height = 3 m

Area = 1/2 x base x height

        = 1/2 x 8 x 3

        = 12 m