Blueprint Builders Slides Blueprint Builders
Mastering Area of Composite Figures
Today's Blueprint
01
Identify and define composite figures .
02
Decompose complex shapes into rectangles, triangles, and semi-circles.
03
Calculate total area using integer measurements.
"Every complex design starts with simple shapes."
The Toolbox
Rectangle
\(A = l \times w\)
Length × Width
\(A = \frac{1}{2} b h\)
Half Base × Height
\(A = \frac{1}{2} \pi r^2\)
Use π ≈ 3.14
The Strategy: Decompose
1
Break it down into simple shapes.
2
Calculate the area of each part.
3
Add them up for the total area!
A
B
Total Area = A + B
Example 1: The Studio
10 cm x 8 cm Height: 6 cm Base = 10 cm
1. Rectangle Area
\(10 \times 8 = 80 \text{ cm}^2\)
2. Triangle Area
\(\frac{1}{2} \times 10 \times 6 = 30 \text{ cm}^2\)
Total Area
\(110 \text{ cm}^2\)
Challenge Time!
Time to test your blueprint skills. Can you calculate the area of these 10 composite figures?
Q1
Rectangle (8x5) + Triangle (base 8, height 4) on top.
A) 40
B) 56
C) 72
D) 48
Q2
Square (10x10) + Semi-circle (r=5) on top. (π=3)
A) 137.5
B) 175
C) 150
D) 125
Blueprint Warnings
Missing Parts
Always check that you have added every shape in the composite figure. Don't leave any piece out!
Radius vs. Diameter
Semi-circle formulas use the radius . If you're given the full width (diameter), cut it in half first!
Mission Complete
Decompose
Calculate
Combine
"Ready to build your masterpiece?"
Blueprint Builders Vocabulary Matchup Blueprint Builders
Vocabulary Match-Up
Name:
Match each term on the left with its definition on the right. Draw a straight line between the dots.
Composite Figure
Decompose
Area
Semi-circle
Formula
Dimension
To break a complex shape down into smaller, simpler parts.
Exactly half of a full circle.
A mathematical rule or expression used for calculations.
The measurement of the surface inside a 2D shape.
A measurement of length, width, or height.
A shape made up of two or more simple geometric shapes.
Architect's Challenge
In your own words, why is it easier to find the area of a "Composite Figure" by decomposing it instead of trying to measure it as one big, complex piece?
Blueprint Builders Practice Quiz Blueprint Builders
Area Assessment
Name:
Instructions: Calculate the total area for each figure. Use π = 3 for semi-circles. Show your work in the provided boxes below each question.
8 × 5 h = 4
1. A rectangle (8 by 5) has a triangle with base 8 and height 4 on top. Total area?
A) 40
B) 56
C) 72
D) 48
Show Work Area:
10 × 10 r = 5
2. A square building (10 by 10) with a semi-circle (r=5) on top. Total area? (Use π=3)
A) 137.5
B) 175
C) 150
D) 125
Show Work Area:
6 × 4 6 × 4
3. A "T" shape made of two identical 6 by 4 rectangles. What is the total area?
A) 24
B) 48
C) 36
D) 60
Show Work Area:
b=12, h=10 r=6
4. A triangle (b=12, h=10) with a semi-circle (r=6) on its base. Area? (Use π=3)
A) 60
B) 54
C) 114
D) 168
Show Work Area:
15 × 10 cut: 6x5
5. A rectangle (15 by 10) with a corner triangle (b=6, h=5) removed. Remaining area?
A) 150
B) 135
C) 165
D) 120
Show Work Area:
8 × 8 r = 4
6. A square (8 by 8) has two semi-circles (r=4) on opposite sides. Area? (Use π=3)
A) 64
B) 112
C) 96
D) 128
Show Work Area:
20 × 10 2 semi ponds removed (r=5)
7. A field (20x10) with 2 semi-circular ponds (r=5) removed. Area left? (Use π=3)
A) 125
B) 200
C) 175
D) 150
Show Work Area:
12 × 4 Roof h = 8
8. A house shape with a 12x4 rectangle base and an 8-unit high triangle roof. Total area?
A) 48
B) 96
C) 72
D) 144
Show Work Area:
b=10, h=6 b=10, h=6
9. A diamond made of two identical triangles, each with base 10 and height 6. Total area?
A) 60
B) 30
C) 120
D) 45
Show Work Area:
12 × 2 r = 6
10. An arch (radius 6 semi-circle) on a 12x2 rectangle. Total area? (Use π=3)
Blueprint Builders Answer Key Blueprint Builders
Teacher Answer Key
Vocabulary Match-Up Keys
Composite Figure A shape made up of two or more simple geometric shapes.
Decompose To break a complex shape down into smaller, simpler parts.
Area The measurement of the surface inside a 2D shape.
Semi-circle Exactly half of a full circle.
Formula A mathematical rule or expression used for calculations.
Dimension A measurement of length, width, or height.
Practice Quiz Keys
Note: Calculations assume π = 3 for all semi-circle problems.
B
Rectangle (8 × 5 = 40) + Triangle (½ × 8 × 4 = 16) = 56
A
Square (10 × 10 = 100) + Semi-circle (½ × 3 × 5² = 37.5) = 137.5
B
Rect 1 (6 × 4 = 24) + Rect 2 (6 × 4 = 24) = 48
C
Triangle (½ × 12 × 10 = 60) + Semi-circle (½ × 3 × 6² = 54) = 114
B
Rectangle (15 × 10 = 150) - Triangle (½ × 6 × 5 = 15) = 135
B
Square (64) + 2 Semi-circles (½ × 3 × 4² × 2 = 48) = 112
A
Rect (200) - 2 Semi-circles (½ × 3 × 5² × 2 = 75) = 125
B
Rect base (48) + Triangle Roof (½ × 12 × 8 = 48) = 96
A
Triangle 1 (30) + Triangle 2 (30) = 60
A
Rect base (24) + Semi-circle arch (½ × 3 × 6² = 54) = 78
