Answer :
To work out the area of the compound shape, we need to calculate the area of each part separately and then add them together. The shape is composed of a rectangle and a triangle.
Calculate the area of the rectangle:
The formula for the area of a rectangle is:
[tex]\text{Area of rectangle} = \text{width} \times \text{height}[/tex]
Given:
- Width = 12 cm
- Height = 10 cm
Substitute the values into the formula:
[tex]\text{Area of rectangle} = 12 \times 10 = 120 \text{ cm}^2[/tex]
Calculate the area of the triangle:
The formula for the area of a triangle is:
[tex]\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height}[/tex]
Given:
- Base = 12 cm
- Height = 8 cm
Substitute the values into the formula:
[tex]\text{Area of triangle} = \frac{1}{2} \times 12 \times 8 = 48 \text{ cm}^2[/tex]
Add the two areas together:
[tex]\text{Total area} = \text{Area of rectangle} + \text{Area of triangle}[/tex]
Substitute the previously calculated areas:
[tex]\text{Total area} = 120 + 48 = 168 \text{ cm}^2[/tex]
Thus, the area of the compound shape is 168 cm².
