To find the total area of the composite figure, we’ll split it into two parts and calculate the area for each, then sum them up. The figure consists of a trapezoid on the left and a triangle on the right.

1. Area of the Trapezoid (Section 1)

For a trapezoid, the area formula is: $A_1 = \frac{1}{2} \times (b_1 + b_2) \times h$ where:

• $b_1 = 20 \, \text{mm}$ (top base),
• $b_2 = 30 \, \text{mm}$ (bottom base),
• $h = 40 \, \text{mm}$ (height).

Substituting the values: $A_1 = \frac{1}{2} \times (20 + 30) \times 40 = \frac{1}{2} \times 50 \times 40 = 1000 \, \text{mm}^2$

2. Area of the Triangle (Section 2)

For a triangle, the area formula is: $A_2 = \frac{1}{2} \times b \times h$ where:

• $b = 15 \, \text{mm}$ (base),
• $h = 16 \, \text{mm}$ (height).

Substituting the values: $A_2 = \frac{1}{2} \times 15 \times 16 = \frac{1}{2} \times 240 = 120 \, \text{mm}^2$

3. Total Area of the Composite Figure

Adding the two areas together: $A_T = A_1 + A_2 = 1000 + 120 = 1120 \, \text{mm}^2$

Answer

The total area, rounded to the nearest tenth, is $\mathbf{1120 \, \text{mm}^2}$. However, none of the provided options match this result, suggesting a possible error in the problem or its answer choices.

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Related Questions

1. How do you calculate the area of a parallelogram?
2. What is the formula for finding the perimeter of a trapezoid?
3. How do you determine the height of a triangle if only the area and base are given?
4. What method would you use to calculate the area of a complex figure with multiple shapes?
5. How can you verify the calculated area of a composite shape?

Tip

Always double-check unit consistency when calculating areas in composite figures to avoid errors.