MathIsimple

Geometry: Area & Volume

Calculate area of polygons and volume of 3D shapes including prisms and cylinders.

7th Grade
Geometry
~45 min
🎮 Interactive Activity: Area Calculator

Calculate the area of different shapes!

rectangle: 8 × 5
🎮 Interactive Activity: Volume Calculator

Calculate the volume of 3D shapes!

prism: 5 × 4 × 3
1. Area Formulas

Common Area Formulas

Area measures the space inside a 2D shape, measured in square units.

Rectangle: A = l × w

Example: length = 8, width = 5

Area = 8 × 5 = 40 square units

Triangle: A = ½ × base × height

Example: base = 10, height = 6

Area = ½ × 10 × 6 = 30 square units

Trapezoid: A = ½(b₁ + b₂) × h

Example: bases = 8 and 12, height = 5

Area = ½(8 + 12) × 5 = 50 square units

Parallelogram: A = base × height

Example: base = 9, height = 5

Area = 9 × 5 = 45 square units

Note: Height is the perpendicular distance, not the length of the hypotenuse

Area Formula Summary:
  • • Rectangle: length × width
  • • Triangle: ½ × base × height
  • • Trapezoid: ½ × (top base + bottom base) × height
  • • Parallelogram: base × height
2. Volume Formulas
3. Surface Area
4. Real-World Applications
5. Problem-Solving Strategies
6. Common Errors & Tips
Frequently Asked Questions

Practice Time!

Practice Quiz
10
Questions
0
Correct
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Score
1
What is the area of a rectangle with length 12 and width 8?
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2
What is the area of a triangle with base 10 and height 6?
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3
What is the volume of a rectangular prism with dimensions 5 × 4 × 3?
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4
What is the area of a trapezoid with bases 8 and 12, height 5?
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5
What is the volume of a cube with edge length 4?
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6
What is the area of a parallelogram with base 9 and height 5?
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7
A cylinder has radius 3 and height 5. What is its volume? (Use π ≈ 3.14)
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8
What is the surface area of a cube with edge 4?
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9
Find the height of a triangle with area 36 and base 9.
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10
What is the volume of a cylinder with radius 2 and height 6? (Use π ≈ 3.14)
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