Final answer:
The area of a triangle with sides measuring 10 inches, 18 inches, and a perimeter of 42 inches is found using Heron's formula. The area is calculated to be approximately 69.65 square inches, which corresponds to option b.
Step-by-step explanation:
To find the area of a triangle with two sides of 10 inches and 18 inches and a perimeter of 42 inches, we first need to determine the length of the third side. The perimeter is the sum of all three sides, so the third side can be found by subtracting the known sides from the total perimeter: 42 inches - (10 inches + 18 inches) = 14 inches for the third side.
Now, we can use Heron's formula to find the semi-perimeter (s), which is half of the perimeter: s = (10 + 18 + 14) / 2 = 21 inches. Next, we apply Heron's formula to find the area (A):
A = √ [s(s - a)(s - b)(s - c)],
where a, b, and c are the lengths of the sides of the triangle.
Plugging in the values: A = √ [21(21 - 10)(21 - 18)(21 - 14)] = √ [21*11*3*7] = √ [4851] ≈ 69.65 in².
So, the area of the given triangle is approximately 69.65 square inches (option b).