Question

In δabc, a = 94 inches, b = 19 inches and c=79 inches. find the area of δabc to the nearest square inch.

a) 705 square inches
b) 372 square inches
c) 897 square inches
d) 989 square inches

Answer 1

To find the area of ΔABC with sides measuring 94 inches, 19 inches, and 79 inches, Heron's formula is used leading to a semi-perimeter of 96 inches. The area is then calculated as approximately 705 square inches, matching option (a).

Step-by-step explanation:

To find the area of ΔABC where side a is 94 inches, side b is 19 inches, and side c is 79 inches, one must use Heron's formula, assuming that these measurements form a valid triangle. Heron's formula states that the area of a triangle can be calculated from its three sides using the following steps:

1. Calculate the semi-perimeter (s) of the triangle using s = (a + b + c) / 2.
2. Compute the area using the formula: Area = √(s(s - a)(s - b)(s - c)) where √ indicates the square root.

First, calculate the semi-perimeter:

s = (94 + 19 + 79) / 2 = 96 inches

Then, calculate the area using Heron's formula:

Area = √(96(96 - 94)(96 - 19)(96 - 79)) = √(96 * 2 * 77 * 17)

After doing the calculations, the area is found to be approximately 705 square inches, which corresponds to option (a).