Area of Polygons

Grade 6 · Math · Study Guide

Learn how to calculate the area of rectangles, triangles, parallelograms, and trapezoids.

Area is the amount of space inside a two-dimensional shape, measured in square units such as cm² or m². Different polygons have different area formulas.

For a rectangle, multiply length times width: A = l × w. For a square, since all sides are equal, A = s². For a parallelogram, multiply the base by the height (the perpendicular height, not the slanted side): A = b × h.

For a triangle, the area is half the product of the base and height: A = ½ × b × h. This is because a triangle is exactly half of a parallelogram with the same base and height. The height of a triangle must be perpendicular to the base.

A trapezoid has two parallel sides called bases, labeled b₁ and b₂. The area formula is A = ½ × (b₁ + b₂) × h, where h is the perpendicular height between the two bases.

When solving area problems, always check your units. If dimensions are in centimeters, the area is in square centimeters. For composite figures (shapes made of multiple polygons), break the shape into simpler parts, find each area, and add them together. Area formulas appear throughout geometry and are essential for real-world applications like flooring, painting, and land measurement.

Key terms

Area
The measure of the space inside a two-dimensional shape, expressed in square units
Base
A side of a polygon used as a reference for calculating area
Height
The perpendicular distance from the base to the opposite side or vertex
Parallelogram
A four-sided figure with two pairs of parallel sides; area = base × height
Trapezoid
A quadrilateral with exactly one pair of parallel sides; area = ½(b₁ + b₂)h
Composite Figure
A shape made up of two or more simple polygons; find total area by adding the areas of each part

Flashcards

Area of a rectangle
A = length × width
Area of a square
A = side × side = s²
Area of a parallelogram
A = base × height (use perpendicular height)
Area of a triangle
A = ½ × base × height
Area of a trapezoid
A = ½ × (b₁ + b₂) × height
Rectangle: l = 7, w = 3
A = 7 × 3 = 21 square units
Triangle: b = 8, h = 5
A = ½ × 8 × 5 = 20 square units
What units is area measured in?
Square units, such as cm², m², or ft²

Questions

  1. A rectangle has a length of 9 cm and a width of 5 cm. What is its area?

    1. 28 cm²
    2. 45 cm²
    3. 40 cm²
    4. 14 cm²
    Show answer

    Answer: 45 cm²

    A = 9 × 5 = 45 cm²

  2. A triangle has a base of 10 m and a height of 6 m. Its area is ___ m².

    Show answer

    Answer: 30

    A = ½ × 10 × 6 = 30 m²

  3. The height of a triangle must be perpendicular to its base.

    Show answer

    Answer: True

    Height in area formulas is always the perpendicular distance from the base

  4. A parallelogram has a base of 8 ft and a height of 4 ft. What is its area?

    1. 16 ft²
    2. 24 ft²
    3. 32 ft²
    4. 12 ft²
    Show answer

    Answer: 32 ft²

    A = 8 × 4 = 32 ft²

  5. A trapezoid has bases of 6 cm and 10 cm, and a height of 4 cm. Its area is ___ cm².

    Show answer

    Answer: 32

    A = ½ × (6 + 10) × 4 = ½ × 16 × 4 = 32 cm²

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