Question

The composite figure has an area of 156 m². The top of the composite is a square with a base of 12 and a side length of 10 so the triangle part has a base of 12 m what would be the height of the triangle.

Answer 1

To find the height of the triangle in the composite figure, we start by breaking down the components of the figure.

1. **Calculate the area of the square:**
The square has a base and height both equal to 10 m (since it's a square).
\[
\text{Area of the square} = \text{side}^2 = 10 \times 10 = 100 \, \text{m}^2
\]

2. **Calculate the area of the triangle:**
Let the height of the triangle be \( h \) meters. The base of the triangle is given as 12 m.
The area of a triangle is given by the formula:
\[
\text{Area of the triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 12 \times h
\]

3. **Total area of the composite figure:**
The total area of the composite figure is the sum of the areas of the square and the triangle.
\[
\text{Total area} = \text{Area of square} + \text{Area of triangle}
\]
Given that the total area is 156 m², we can set up the equation:
\[
156 = 100 + \frac{1}{2} \times 12 \times h
\]

4. **Solve for \( h \):**
First, simplify the equation:
\[
156 - 100 = \frac{1}{2} \times 12 \times h
\]
\[
56 = \frac{1}{2} \times 12 \times h
\]
\[
56 = 6h
\]
\[
h = \frac{56}{6} \approx 9.33 \, \text{m}
\]

Thus, the height of the triangle is approximately **9.33 meters**.