A statue is erected on a triangular marble base. The lengths of the sides of the triangle are 12 feet, 16 feet, and 18 feet. What is the area of the region at the base of the statue to the nearest square foot?
169 ft2
144 ft2
143 ft2
94 ft2
Just use Heron's formula:
A = √((23)(23-12)(23-16)(23-18))
To find the area of the region at the base of the statue, we need to find the area of the triangular base.
We can use Heron's formula to find the area of a triangle when we know the lengths of its sides. Heron's formula states that the area (A) of a triangle with side lengths a, b, and c is given by:
A = sqrt(s * (s - a) * (s - b) * (s - c))
where s is the semiperimeter of the triangle, given by:
s = (a + b + c) / 2
For this triangle with side lengths 12 ft, 16 ft, and 18 ft, we can calculate the semiperimeter:
s = (12 + 16 + 18) / 2 = 46 / 2 = 23 ft
Now we can calculate the area of the triangle using Heron's formula:
A = sqrt(23 * (23 - 12) * (23 - 16) * (23 - 18))
A = sqrt(23 * 11 * 7 * 5)
A = sqrt(8855)
A ≈ 94 ft²
Therefore, the area of the region at the base of the statue is approximately 94 square feet.