5A Area Formulas Study Guide

Key Vocabulary

Area — the amount of space inside a flat (2D) shape, measured in square units. (área)

Base (b) — the bottom side of a shape (or any side you choose to measure from). (base)

Height (h) — the perpendicular distance from the base to the top. (altura)

Parallelogram — a four-sided shape with two pairs of parallel sides. (paralelogramo)

Triangle — a three-sided shape. (triángulo)

Trapezoid — a four-sided shape with exactly one pair of parallel sides. (trapecio)

Rectangle

  +----------+
  |          | h = 4
  |          |
  +----------+
    b = 8

A = b × h = 8 × 4 = 32 sq units

Parallelogram

    +----------+
   /          /  h = 5
  /          / |
 +----------+
    b = 10

A = b × h = 10 × 5 = 50 sq units

Triangle

      /\
     /  \  h = 6
    /    \|
   +------+
    b = 8

A = ½ × b × h
  = ½ × 8 × 6 = 24 sq units

Trapezoid

    +------+  b1 = 6
   /        \
  /    h=4   \
 +------------+  b2 = 10

A = ½ × (b1 + b2) × h
  = ½ × (6+10) × 4
  = ½ × 16 × 4 = 32 sq units

1 Identify the shape (rectangle, parallelogram, triangle, or trapezoid).
2 Find the base and height from the diagram. Height is ALWAYS perpendicular (makes a 90° angle).
3 Choose the correct formula for that shape.
4 Substitute and solve. Include square units in your answer.

Rectangle: A = l × w

Parallelogram: A = b × h

Triangle: A = ½ × b × h

Trapezoid: A = ½ × (b₁ + b₂) × h

Height is ALWAYS perpendicular to the base (straight up and down, making a 90° angle). The slanted side is NOT the height!
A triangle is HALF a parallelogram. That is why we multiply by ½.
Don’t forget square units! Area is always in square units (cm², ft², m²).
Trapezoid has TWO bases. Add them together before multiplying.

1. Find the area of a rectangle with length 12 cm and width 5 cm.

2. Find the area of a parallelogram with base 9 in. and height 7 in.

3. Find the area of a triangle with base 10 ft and height 6 ft.

4. Find the area of a trapezoid with bases 5 m and 9 m and height 4 m.