📐 Geometry Practice Problems

Master geometric concepts with interactive exercises and visualizations

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🔺 Basic Shapes & Properties

Find the area of a rectangle with length 8 cm and width 5 cm

Area =
Hint: Area = length × width

Find the perimeter of a square with side length 6 cm

Perimeter =
Hint: Perimeter = 4 × side length

What is the sum of interior angles in a triangle?

Hint: All triangles have the same angle sum

📐 Triangle Properties & Calculations

Classify this triangle by its angles: angles 30°, 60°, 90°

Hint: Look for a 90° angle

Find the area of a triangle with base 10 cm and height 6 cm

Area =
Hint: Area = (base × height) ÷ 2

Use Pythagorean theorem: legs 3 and 4, find hypotenuse

Hypotenuse =
Hint: a² + b² = c², where c is the hypotenuse

Find missing angle: angles given are 45° and 60°

Third angle =
Hint: Angles in a triangle sum to 180°

🔲 Quadrilateral Properties

Find area of a parallelogram: base 12 cm, height 8 cm

Area =
Hint: Area = base × height (same as rectangle)

Find area of a trapezoid: parallel sides 8 cm and 12 cm, height 5 cm

Area =
Hint: Area = (sum of parallel sides × height) ÷ 2

What property do opposite angles in a parallelogram have?

Hint: Opposite sides are also equal and parallel

⭕ Circle Calculations

Find circumference of a circle with radius 7 cm

Circumference ≈
Hint: C = 2πr (use π ≈ 3.14)

Find area of a circle with diameter 10 cm

Area ≈
Hint: First find radius (diameter ÷ 2), then A = πr²

Find the measure of a central angle that intercepts an arc of 60°

Central angle =
Hint: Central angle equals intercepted arc

📦 3D Shapes & Volume

Find volume of a cube with side length 4 cm

Volume =
Hint: Volume = side³

Find volume of a rectangular prism: 5 × 3 × 7 cm

Volume =
Hint: Volume = length × width × height

Find surface area of a sphere with radius 3 cm

Surface Area ≈
Hint: Surface Area = 4πr²

🔄 Transformations

Point A(2,3) is translated 4 units right and 2 units up. Find A'

A' = ( , )
Hint: Add translation values to coordinates

Point B(-1,4) is reflected over the x-axis. Find B'

B' = ( , )
Hint: x stays the same, y becomes negative

Point C(3,1) is rotated 90° clockwise around origin. Find C'

C' = ( , )
Hint: 90° clockwise: (x,y) → (y,-x)

📍 Coordinate Geometry

Find distance between points (2,3) and (5,7)

Distance =
Hint: Use distance formula: √[(x₂-x₁)² + (y₂-y₁)²]

Find slope of line through (1,2) and (4,8)

Slope =
Hint: Slope = (y₂-y₁)/(x₂-x₁)

Write equation of line with slope 3 through (2,5)

y =
Hint: Use point-slope form: y - y₁ = m(x - x₁)

📊 Your Geometry Practice Summary

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📄 practice-geometry.html | 2025-12-26