500 yd

300 yd

400 yd

What is the area of the triangular field in square feet?

A 60,000 ft

B 120,000 ft2

C 540,000 12

D 1,080,000 ft2

The correct answer is option (A) 60,000 ft.

Step-by-step Explanation: In a triangle with all three sides given and no vertical height, we shall not apply the conventional (commonly used) formulae which is

Area = 1/2 B x H

Rather we shall apply the Heron’s Formulae which states as follows;

Area = [square root] s(s - a)(s - b)(s - b)

Where a, b and c are the three sides and a is the semi-perimeter.

We shall start with the semi-perimeter which is

s = (300 + 400 + 500)/2

s = 1200/2

s = 600

Therefore applying the Heron’s formula, the area is calculated as

A = [square root] 600(600 - 500)(600 - 400)(600 - 300)

A = [square root] 600 (100)(200)(300)

A = [square root] 3600000000

A = 60000

The area of the given triangle is 60,000 ft.