Since the user has set both `ExplainAnswer` and `TeachTopic` to false, I will proceed directly to solving the problems shown in the image and providing the final answers.
The image contains 6 problems asking for the area of shaded regions in compound figures. I will solve each one step-by-step.
Problem 1:
*
Shape: A rectangle attached to a semicircle.
*
Rectangle: Length = 12, Width = 5.
* Area = $12 \times 5 = 60$.
*
Semicircle: The diameter is the width of the rectangle, which is 5. So, radius $r = 2.5$.
* Area = $\frac{1}{2} \times \pi \times r^2 = 0.5 \times 3.14159 \times (2.5)^2 = 0.5 \times 3.14159 \times 6.25 \approx 9.817$.
*
Total Area: $60 + 9.817 = 69.817$.
*
Rounding: To two decimal places $\rightarrow$
69.82.
Problem 2:
*
Shape: A triangle attached to a semicircle.
*
Triangle: Base = 10 (the vertical line), Height = 12 (horizontal distance).
* Area = $\frac{1}{2} \times \text{base} \times \text{height} = 0.5 \times 10 \times 12 = 60$.
*
Semicircle: Diameter = 10, so radius $r = 5$.
* Area = $\frac{1}{2} \times \pi \times r^2 = 0.5 \times 3.14159 \times 25 \approx 39.27$.
*
Total Area: $60 + 39.27 = 99.27$.
*
Rounding: To two decimal places $\rightarrow$
99.27.
Problem 3:
*
Shape: An arrow shape made of a rectangle and a triangle.
*
Rectangle: Length = 14, Width = 5.
* Area = $14 \times 5 = 70$.
*
Triangle: Base = 10 (vertical side), Height = 4 (horizontal distance).
* Area = $\frac{1}{2} \times 10 \times 4 = 20$.
*
Total Area: $70 + 20 = 90$.
*
Rounding: To two decimal places $\rightarrow$
90.00.
Problem 4:
*
Shape: An L-shaped polygon. We can split this into two rectangles.
*
Rectangle A (Top): Width = 4, Height = 3.
* Area = $4 \times 3 = 12$.
*
Rectangle B (Bottom): Width = 3, Height = 7.
* Area = $3 \times 7 = 21$.
*
Total Area: $12 + 21 = 33$.
*
Rounding: To two decimal places $\rightarrow$
33.00.
Problem 5:
*
Shape: An L-shaped polygon. Split into two rectangles.
*
Rectangle A (Top): Width = 4, Height = 2.
* Area = $4 \times 2 = 8$.
*
Rectangle B (Bottom): Width = 3, Height = 6.
* Area = $3 \times 6 = 18$.
*
Total Area: $8 + 18 = 26$.
*
Rounding: To two decimal places $\rightarrow$
26.00.
Problem 6:
*
Shape: A large rectangle with a triangle cut out from the bottom.
*
Large Rectangle: Width = 6, Height = 13.
* Area = $6 \times 13 = 78$.
*
Triangle (Cutout): Base = 6, Height = 4.
* Area = $\frac{1}{2} \times 6 \times 4 = 12$.
*
Shaded Area: $78 - 12 = 66$.
*
Rounding: To two decimal places $\rightarrow$
66.00.
Final Answer:
1. 69.82
2. 99.27
3. 90.00
4. 33.00
5. 26.00
6. 66.00
Parent Tip: Review the logic above to help your child master the concept of area of compound figures worksheet.
