Question

What is the area of this figure?

a big 3d shape is shown
divided into 3 different shapes with the following measurements
Shape 1
The top is 9 in
The first left side is 2 in
The 1st bottom is 3 in
The 2nd Shape
2nd Left side is 4 in
2nd bottom is 4 in
The 3rd Shape
3rd left side is 3 in
bottom is 2 in
Every Shape
the right side is 9 in

find the area of those 3 shapes then add them up and put the answer in square inches

Answer 1

To find the total area of the three shapes described, we need to calculate the area of each shape individually and then sum them up.

Let's assign each shape as follows:

1. **Shape 1**: A trapezoid with a top base of 9 inches, a bottom base of 3 inches, and a height of 2 inches.
2. **Shape 2**: A rectangle with a width of 4 inches and a height of 4 inches.
3. **Shape 3**: A rectangle with a width of 2 inches and a height of 3 inches.

We will calculate the area for each shape.

### Shape 1: Trapezoid
The area \( A \) of a trapezoid is calculated using the formula:
\[
A = \frac{1}{2} \times (b_1 + b_2) \times h
\]
where
- \( b_1 \) is the length of the top base (9 inches),
- \( b_2 \) is the length of the bottom base (3 inches),
- \( h \) is the height (2 inches).

Plugging in the values:
\[
A_1 = \frac{1}{2} \times (9 + 3) \times 2 = \frac{1}{2} \times 12 \times 2 = 12 \text{ square inches}
\]

### Shape 2: Rectangle
The area \( A \) of a rectangle is calculated using the formula:
\[
A = \text{width} \times \text{height}
\]
Here, the width is 4 inches and the height is 4 inches.
\[
A_2 = 4 \times 4 = 16 \text{ square inches}
\]

### Shape 3: Rectangle
For Shape 3, again using the rectangle area formula:
Here, the width is 2 inches and the height is 3 inches.
\[
A_3 = 2 \times 3 = 6 \text{ square inches}
\]

### Total Area
Now, we sum the areas of all three shapes:
\[
\text{Total Area} = A_1 + A_2 + A_3 = 12 + 16 + 6 = 34 \text{ square inches}
\]

Thus, the total area of the figure is **34 square inches**.