Question

What is the area of the triangle shown below?
A triangle. The base is 12 units and the other 2 side lengths are 10 units each. The bottom left angle and bottom right angle are congruent.



units

Answer 1

To find the area of the triangle with a base of 12 units and two equal sides of 10 units each, we can use the formula for the area of a triangle:

\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]

First, we need to find the height of the triangle. Since the triangle is isosceles (two sides are equal), we can drop a perpendicular from the top vertex to the middle of the base. This creates two right triangles.

1. **Find the length of half the base:**
The half of the base is:
\[
\frac{12}{2} = 6 \text{ units}
\]

2. **Use the Pythagorean theorem to find the height:**
In the right triangle formed, we have:
- The hypotenuse (one of the sides of the triangle) = 10 units
- One leg (half the base) = 6 units
- The other leg is the height (h) we want to find.

We can apply the Pythagorean theorem:
\[
h^2 + 6^2 = 10^2
\]
\[
h^2 + 36 = 100
\]
\[
h^2 = 100 - 36
\]
\[
h^2 = 64
\]
\[
h = \sqrt{64} = 8 \text{ units}
\]

3. **Calculate the area of the triangle:**
Now we can substitute the base and the height into the area formula:
\[
\text{Area} = \frac{1}{2} \times 12 \times 8
\]
\[
\text{Area} = \frac{1}{2} \times 96
\]
\[
\text{Area} = 48 \text{ square units}
\]

Thus, the area of the triangle is \( \boxed{48} \) square units.