Composite Shapes and Their Formulas | Grade 8 and 9 Math Worksheet

Choose a shape. Read the short idea, then click the card to open solved examples and practice questions.

Area

Rectangle + Semicircle

Made from one rectangle and half a circle.

A = lb + ½πr²
Area

Rectangle + Triangle

Made from one rectangle and one triangle.

A = lb + ½bh
Area

Two Semicircles + Rectangle

Two semicircles combine to make one full circle.

A = lb + πr²
Area

Annulus / Ring

Made from a big circle with a smaller circle removed.

A = π(R² − r²)

Rectangle + Semicircle

Find the rectangle area first. Then find half of the circle area. Add both parts.
Solved Examples
Example 1: l = 10, b = 6, r = 3
l = 10 b = 6 r = 3
  1. Rectangle area = 10 × 6 = 60.
  2. Semicircle area = ½ × 3.14 × 3² = 14.13.
  3. Total area = 60 + 14.13 = 74.13.
Answer: 74.13 cm²
Example 2: l = 12, b = 8, r = 4
l = 12 b = 8 r = 4
  1. Rectangle area = 12 × 8 = 96.
  2. Semicircle area = ½ × 3.14 × 4² = 25.12.
  3. Total area = 96 + 25.12 = 121.12.
Answer: 121.12 cm²
Example 3: l = 16, b = 10, r = 5
l = 16 b = 10 r = 5
  1. Rectangle area = 16 × 10 = 160.
  2. Semicircle area = ½ × 3.14 × 5² = 39.25.
  3. Total area = 160 + 39.25 = 199.25.
Answer: 199.25 cm²

Auto-Checked Practice

Rectangle + Triangle

Find the rectangle area. Then find the triangle area using ½ × base × height.
Solved Examples
Example 1: rectangle 8×5, triangle base 5 height 6
l = 8 b = 5 h = 6
  1. Rectangle area = 8 × 5 = 40.
  2. Triangle area = ½ × 5 × 6 = 15.
  3. Total area = 40 + 15 = 55.
Answer: 55 cm²
Example 2: rectangle 12×7, triangle base 7 height 8
l = 12 b = 7 h = 8
  1. Rectangle area = 12 × 7 = 84.
  2. Triangle area = ½ × 7 × 8 = 28.
  3. Total area = 84 + 28 = 112.
Answer: 112 cm²
Example 3: rectangle 15×10, triangle base 10 height 12
l = 15 b = 10 h = 12
  1. Rectangle area = 15 × 10 = 150.
  2. Triangle area = ½ × 10 × 12 = 60.
  3. Total area = 150 + 60 = 210.
Answer: 210 cm²

Auto-Checked Practice

Two Semicircles + Rectangle

Two semicircles make one complete circle, so use πr² only once.
Solved Examples
Example 1: l = 12, b = 6, r = 3
l = 12 r = 3 r = 3
  1. Rectangle area = 12 × 6 = 72.
  2. The two semicircles form one circle.
  3. Circle area = 3.14 × 3² = 28.26.
  4. Total area = 72 + 28.26 = 100.26.
Answer: 100.26 cm²
Example 2: l = 15, b = 8, r = 4
l = 15 r = 4 r = 4
  1. Rectangle area = 15 × 8 = 120.
  2. The two semicircles form one full circle.
  3. Circle area = 3.14 × 4² = 50.24.
  4. Total area = 120 + 50.24 = 170.24.
Answer: 170.24 cm²
Example 3: l = 20, b = 10, r = 5
l = 20 r = 5 r = 5
  1. Rectangle area = 20 × 10 = 200.
  2. The two semicircles form one full circle.
  3. Circle area = 3.14 × 5² = 78.5.
  4. Total area = 200 + 78.5 = 278.5.
Answer: 278.5 cm²

Auto-Checked Practice

Annulus / Ring Shape

Find the big circle area. Find the small circle area. Subtract the small circle from the big circle.
Solved Examples
Example 1: R = 6, r = 3
R = 6 r = 3
  1. Big circle area = 3.14 × 6² = 113.04.
  2. Small circle area = 3.14 × 3² = 28.26.
  3. Ring area = 113.04 − 28.26 = 84.78.
Answer: 84.78 cm²
Example 2: R = 8, r = 4
R = 8 r = 4
  1. Big circle area = 3.14 × 8² = 200.96.
  2. Small circle area = 3.14 × 4² = 50.24.
  3. Ring area = 200.96 − 50.24 = 150.72.
Answer: 150.72 cm²
Example 3: R = 10, r = 5
R = 10 r = 5
  1. Big circle area = 3.14 × 10² = 314.
  2. Small circle area = 3.14 × 5² = 78.5.
  3. Ring area = 314 − 78.5 = 235.5.
Answer: 235.5 cm²

Auto-Checked Practice