Compound Shapes Simplified Worksheet
Area of Compound Shapes
Step-by-Step Guide: Split the shape, find each area, and add them together!
Math Support
Name:
Date:
Period:
Rectangle
\( \text{Area} = \text{base} \times \text{height} \)
Multiply width × height
Triangle
\( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \)
Multiply base × height ÷ 2
Semi-Circle
\( \text{Area} = 0.5 \times 3.14 \times r \times r \)
Remember: \( \text{radius } r = \text{diameter} \div 2 \)
PROBLEM 1 (GUIDED)
The House Shape
Rectangle + Triangle
Shape A: Rectangle Shape B: Triangle h = 4 m base = 8 m 5 m Split at the red dashed line!
Step 1: Find Area of Shape A (Blue Rectangle)
Area = 8 × 5 = 40 m²
Step 2: Find Area of Shape B (Green Triangle)
Area = 0.5 × 8 × 4 = 16 m²
Step 3: Add Both Areas Together 40 m² + 16 m²
Total Area =
56 m²
PROBLEM 2
The Silo Tower
Rectangle + Semi-Circle
Shape B: Semi-Circle Shape A: Rectangle base = 6 cm 9 cm diameter = 6 cm Radius = 6 ÷ 2 = 3 cm
Step 1: Area of Shape A (Blue Rectangle)
Area =
×
=
cm²
Step 2: Area of Shape B (Amber Semi-Circle)
0.5 × 3.14 ×
×
=
cm²
Hint: \( 0.5 \times 3.14 \times 3 \times 3 = 14.13 \)
Step 3: Add Areas Together Shape A + Shape B
Total =
cm²
Rule to remember: Always cut the shape into simple pieces you know! Page 1 of 2
Practice Lab: You Try It!
Use your 3-step strategy: 1. Shape A → 2. Shape B → 3. Add together.
Student: PAGE 2
PROBLEM 3
The Barn Roof Wall
Rectangle + Triangle
Shape A: Rectangle Shape B: Triangle h = 5 ft base = 10 ft 6 ft Both shapes share the 10 ft base!
Step 1: Area of Shape A (Rectangle)
\( A = b \times h = \)
×
=
ft²
Step 2: Area of Shape B (Triangle)
\( A = 0.5 \times \)
×
=
ft²
Step 3: Total Area Add Shape A + Shape B:
ft²
PROBLEM 4
The Arch Window
Rectangle + Semi-Circle
Shape B: Semi-Circle Shape A: Rectangle width = 8 in 7 in diameter = 8 in Radius = 8 ÷ 2 = 4 in
Step 1: Area of Shape A (Rectangle)
\( A = b \times h = \)
×
=
in²
Step 2: Area of Shape B (Semi-Circle)
0.5 × 3.14 ×
×
=
in²
Hint: \( 0.5 \times 3.14 \times 4 \times 4 = 25.12 \)
Step 3: Total Area Add Shape A + Shape B:
in²
My Checklist: Found Area A Found Area B Added together
Page 2 of 2
