The figure in the image appears to be composed of two distinct shapes: a trapezoid on top and a triangle on the bottom. To find the total area, we will calculate the areas of these two shapes separately and then sum them.

1. Area of the trapezoid:

A trapezoid's area is given by the formula: $A_{\text{trapezoid}} = \frac{1}{2} \times (b_1 + b_2) \times h$ Where:

• $b_1$ and $b_2$ are the lengths of the parallel sides (bases).
• $h$ is the height of the trapezoid.

From the image:

• $b_1 = 8 \, \text{in}$ (bottom base of the trapezoid).
• $b_2 = 4 \, \text{in}$ (top base of the trapezoid).
• $h = 8 \, \text{in}$ (height of the trapezoid).

Substituting the values: $A_{\text{trapezoid}} = \frac{1}{2} \times (8 + 4) \times 8 = \frac{1}{2} \times 12 \times 8 = 48 \, \text{in}^2$

2. Area of the triangle:

The area of a triangle is given by the formula: $A_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height}$ From the image:

• Base = $8 \, \text{in}$.
• Height = $6 \, \text{in}$.

Substituting the values: $A_{\text{triangle}} = \frac{1}{2} \times 8 \times 6 = 24 \, \text{in}^2$

3. Total Area:

Now, sum the areas of the trapezoid and the triangle: $\text{Total Area} = A_{\text{trapezoid}} + A_{\text{triangle}} = 48 \, \text{in}^2 + 24 \, \text{in}^2 = 72 \, \text{in}^2$

However, the closest available option to 72 square inches on the screen appears to be 58 in², which suggests that either some measurements might be off or there is a minor discrepancy in the problem setup. Would you like to discuss this further or clarify any part?

5 Related Questions:

1. How do you calculate the area of other quadrilaterals, like parallelograms or rectangles?
2. How do the properties of different polygons affect their area calculations?
3. How can the area of a composite figure be broken down in general cases?
4. Could there be other approaches to calculate the area of irregular shapes?
5. What is the difference between the area formulas for 2D shapes like triangles, trapezoids, and circles?

Tip:

When working with composite shapes, always ensure all dimensions are accurately labeled and use the correct formula for each component shape.