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?

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.

First, we calculate the semi-perimeter \( s \) of the triangle:

\[
s = \frac{a + b + c}{2} = \frac{5 + 7 + 10}{2} = \frac{22}{2} = 11 \text{ meters}
\]

Next, we apply Heron's formula to find the area \( A \):

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

Substituting the values of \( a = 5 \), \( b = 7 \), and \( c = 10 \):

\[
A = \sqrt{11(11-5)(11-7)(11-10)} = \sqrt{11 \times 6 \times 4 \times 1}
\]

Calculating the products step by step:

\[
A = \sqrt{11 \times 6 \times 4} = \sqrt{264}
\]

Now we compute \( \sqrt{264} \):

\[
\sqrt{264} \approx 16.2481
\]

Rounding to the nearest tenth, the area of the triangular plot of land is:

\[
\boxed{16.2} \text{ square meters}
\]