Question

Use Heron's formula to find the area of the triangle. Round to the nearest square foot.Side a=7 feetSide b=7 feetSide c=5 feet

Answer 1

The area is approximately 16 square feet.

Step - by -Step Explanation

What to find? Area of the triangle using Heron's formula.

Given:

• Side a=7 feet

,

• Side b=7 feet

,

• Side c=5 feet

The Heron's formula is given below:

`\text{Area}=\sqrt[]{p(p-a)(p-b)(p-c)}`

Where P is the perimeter of the triangle.

a, b and c are the sides of the triangle.

We need to first find the half perimeter of the triangle.

P = a+b+c /2

= 7+7+5 /2=19/2 = 9.5

Substitute the value of p, a, b and c into the formula and simplify.

`\text{Area}=\sqrt[]{9.5(9.5-7)(9.5-7)(9.5-5)}`
`=\sqrt[]{9.5*2.5*2.5*4.5}`
`=\sqrt[]{267.1875}`
`\approx16\text{ square f}eet`

Hence, the area of the triangle is approximately 16 square feet.