To find the height of the triangle in the composite figure, we can use the information about the area of the entire figure.
The area of the rectangle can be calculated using the formula:
\[ \text{Area of Rectangle} = \text{width} \times \text{height} \]
Given that the top side of the rectangle is 12 meters and the right side (height) is 10 meters, the area of the rectangle is:
\[ \text{Area of Rectangle} = 12 \text{ m} \times 10 \text{ m} = 120 \text{ m}^2 \]
Let \( h \) be the height of the triangle. The area of the triangle can be calculated using the formula:
\[ \text{Area of Triangle} = \frac{1}{2} \times \text{base} \times \text{height} \]
The base of the triangle is the same as the width of the rectangle, which is 12 meters. Therefore, the area of the triangle is:
\[ \text{Area of Triangle} = \frac{1}{2} \times 12 \text{ m} \times h = 6h \text{ m}^2 \]
The total area of the composite figure is given as 156 square meters. Thus, we set up the equation:
\[ \text{Area of Rectangle} + \text{Area of Triangle} = 156 \text{ m}^2 \]
Substituting the areas we calculated:
\[ 120 \text{ m}^2 + 6h \text{ m}^2 = 156 \text{ m}^2 \]
Now, we solve for \( h \):
\[ 6h = 156 - 120 \] \[ 6h = 36 \] \[ h = \frac{36}{6} = 6 \text{ m} \]
Thus, the height of the triangle is 6 meters.
Correct answer: 6 meters.
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