Question

in a drawing the first block is a square3‘ x 3‘. The second section is a rectangle8 x 3‘. The third section is a triangle 8’ x 3’ indicate the total area of the composite figure

Answer 1

To find the total area of the composite figure composed of a square, a rectangle, and a triangle, we will calculate the area for each shape separately and then sum them up.

1. **Area of the Square:**
The area of a square is given by the formula:
\[
\text{Area} = \text{side} \times \text{side}
\]
For a square with each side measuring 3 feet:
\[
\text{Area of the square} = 3 \, \text{ft} \times 3 \, \text{ft} = 9 \, \text{ft}^2
\]

2. **Area of the Rectangle:**
The area of a rectangle is given by the formula:
\[
\text{Area} = \text{length} \times \text{width}
\]
For a rectangle measuring 8 feet by 3 feet:
\[
\text{Area of the rectangle} = 8 \, \text{ft} \times 3 \, \text{ft} = 24 \, \text{ft}^2
\]

3. **Area of the Triangle:**
The area of a triangle is given by the formula:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]
Here, taking the base as 8 feet and the height as 3 feet:
\[
\text{Area of the triangle} = \frac{1}{2} \times 8 \, \text{ft} \times 3 \, \text{ft} = \frac{1}{2} \times 24 \, \text{ft}^2 = 12 \, \text{ft}^2
\]

4. **Total Area of the Composite Figure:**
Now, we add the areas of all three shapes:
\[
\text{Total Area} = \text{Area of the square} + \text{Area of the rectangle} + \text{Area of the triangle}
\]
\[
\text{Total Area} = 9 \, \text{ft}^2 + 24 \, \text{ft}^2 + 12 \, \text{ft}^2 = 45 \, \text{ft}^2
\]

Therefore, the total area of the composite figure is **45 square feet**.