Question

What is the area of the triangle? Remember, area is always in square units so use that in your answer too!
11cm
25 cm
16cm

Answer 1

To find the area of a triangle when you know the lengths of all three sides, you can use Heron's formula.

1. First, calculate the semi-perimeter \( s \):

\[
s = \frac{a + b + c}{2}
\]

where \( a = 11 \) cm, \( b = 25 \) cm, and \( c = 16 \) cm.

\[
s = \frac{11 + 25 + 16}{2} = \frac{52}{2} = 26 \text{ cm}
\]

2. Now, use Heron’s formula to find the area \( A \):

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

Calculating each term:

- \( s - a = 26 - 11 = 15 \) cm
- \( s - b = 26 - 25 = 1 \) cm
- \( s - c = 26 - 16 = 10 \) cm

Now substitute these values into Heron's formula:

\[
A = \sqrt{26 \times 15 \times 1 \times 10}
\]

Calculating the product inside the square root:

\[
26 \times 15 = 390
\]
\[
390 \times 1 = 390
\]
\[
390 \times 10 = 3900
\]

Now take the square root:

\[
A = \sqrt{3900}
\]

Calculating \( \sqrt{3900} \):

\[
\sqrt{3900} \approx 62.45 \text{ cm}^2
\]

Thus, the area of the triangle is approximately \( 62.45 \text{ cm}^2 \).

Final answer:

The area of the triangle is approximately \( 62.45 \text{ cm}^2 \).