Question

A triangular plot of land has sides that measure 5 meters, 7 meters, and 10 meters. What is the area of this plot of land, to the nearest tenth of a square meter?

Question 5 options:

16.7 sq meters


18.2 sq meters


13.2 sq meters


16.2 sq meters

Answer 1

To find the area of a triangular plot of land with sides measuring 5 meters, 7 meters, and 10 meters, we can use Heron's formula, which is given by:

\[
A = \sqrt{s(s-a)(s-b)(s-c)}
\]

where \(s\) is the semi-perimeter of the triangle, and \(a\), \(b\), and \(c\) are the lengths of the sides.

1. First, calculate the semi-perimeter \(s\):
\[
s = \frac{a + b + c}{2} = \frac{5 + 7 + 10}{2} = \frac{22}{2} = 11 \text{ meters}
\]

2. Now, apply Heron's formula:
\[
A = \sqrt{s(s-a)(s-b)(s-c)}
\]

Substitute the values:
\[
A = \sqrt{11(11-5)(11-7)(11-10)}
\]
\[
A = \sqrt{11 \times 6 \times 4 \times 1}
\]
\[
A = \sqrt{11 \times 24}
\]
\[
A = \sqrt{264}
\]
Calculating the square root:
\[
A \approx 16.248
\]

To the nearest tenth, the area of the triangular plot of land is approximately 16.2 square meters.

Thus, the answer is:
**16.2 sq meters**