Problem

Use Heron's formula to find the area of the triangle. Round to the nearest square foot.
Side $a=6$ feet
Side $b=6$ feet
Side $c=4$ feet
The area is approximately square feet.

Answer

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Answer

Final Answer: The area of the triangle is approximately \(\boxed{11}\) square feet.

Steps

Step 1 :Given a triangle with side lengths $a = 6$, $b = 6$, and $c = 4$ feet.

Step 2 :We can use Heron's formula to find the area of the triangle. Heron's formula is given by: \[Area = \sqrt{s(s - a)(s - b)(s - c)}\] where $s$ is the semi-perimeter of the triangle, calculated as $(a + b + c) / 2$.

Step 3 :First, we calculate the semi-perimeter $s = (a + b + c) / 2 = (6 + 6 + 4) / 2 = 8.0$ feet.

Step 4 :Substitute $s = 8.0$, $a = 6$, $b = 6$, and $c = 4$ into Heron's formula, we get: \[Area = \sqrt{8.0(8.0 - 6)(8.0 - 6)(8.0 - 4)} = 11.313708498984761\] square feet.

Step 5 :Round the area to the nearest square foot, we get: \[Area = \text{round}(11.313708498984761) = 11\] square feet.

Step 6 :Final Answer: The area of the triangle is approximately \(\boxed{11}\) square feet.

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