Question

Use a geometric formula to solve the problem. A triangle has a height of 8 feet and an area of 48 square feet. Find the base.

Answer 1

The formula for finding area of a triangle is:

$\frac{1}{2}bh$

The base is 8 feet. The area is 48 ft². Put that into the formula:

$\frac{1}{2} b8 = 48$

Remember that you have to multiply the base × height by $\frac{1}{2}$, which is the same as dividing by 2. To find the height, you need to multiply the area by 2, instead of dividing.

$Area = 48 sq\ ft^{2} \\ 48 \times 2 = 96$

That means the base × height is equal to 96. You already know the height. To find the base, divide the (base × height) by the height. The height is 8.

$96 \div 8 = 12$

That means the base of the triangle is 12 ft

CHECK

$\frac{1}{2}bh$

Base = 12

Height = 8

Put that into the formula:

$12 \cdot 8 \cdot \frac{1}{2} = 96 \cdot \frac{1}{2} = 96 \div 2 = 48$ ✔

BASE = 12 ft