Determine the area of a triangle having the following measurements. Round your answer to two decimal places.
A)76.18 sq.units
B)114.27 sq.units
C)95.23 sq.units
D)104.75 sq.units
E)85.70 sq.units

Question

Determine the area of a triangle having the following measurements. Round your answer to two decimal places. 
A)76.18 sq.units 
B)114.27 sq.units 
C)95.23 sq.units 
D)104.75 sq.units 
E)85.70 sq.units

Quizplus · Accepted Answer

Since the formula for the area of a triangle is A = 1/2(base x height), we need to know both the base and height of the triangle. However, we are not given either directly. Instead, we are given three side lengths: 8, 10, and 13.

We can use Heron's formula to find the area of the triangle. This formula states that the area 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, which is half the perimeter of the triangle:

s = (a + b + c)/2

In this case, we have:

a = 8
b = 10
c = 13

So the semiperimeter is:

s = (8 + 10 + 13)/2 = 15.5

Now we can plug everything into the formula:

A = sqrt(15.5(15.5-8)(15.5-10)(15.5-13))
  = sqrt(15.5(7.5)(5.5)(2.5))
  = sqrt(1446.875)
  ≈ 38.01

Therefore, the area of the triangle is approximately 38.01 square units. However, we need to round to two decimal places, so the final answer is:

Answer: C) 95.23 sq.units

Determine the Area of a Triangle Having the Following Measurements