Overview
This lecture explains how to calculate the area of a triangle using the area formula and provides step-by-step examples.
Area Formula for Triangles
- The area of a triangle is the amount of space inside a two-dimensional triangle.
- The formula for area is: area = base × height ÷ 2.
- In the formula, "base" (b) is the length of the triangle's base, and "height" (h) is the perpendicular height.
- Side-by-side letters in math (bh) mean multiplication.
Example Problems
- Example 1: Base = 5 inches, Height = 12 inches; Area = (5 × 12) ÷ 2 = 60 ÷ 2 = 30 square inches.
- Example 2: Base = 14 meters, Height = 5 meters; Area = (14 × 5) ÷ 2 = 70 ÷ 2 = 35 square meters.
- Example 3: Base = 9 feet, Height = 3 feet; Area = (9 × 3) ÷ 2 = 27 ÷ 2 = 13.5 square feet.
- Example 4: Base = 5 yards, Height = 6 yards; Area = (5 × 6) ÷ 2 = 30 ÷ 2 = 15 square yards.
Why Divide by 2?
- A triangle is half the area of a rectangle or parallelogram with the same base and height.
- Dividing by 2 adjusts for only using half of the rectangle's area.
Key Terms & Definitions
- Area — the amount of space inside a two-dimensional shape.
- Base (b) — the bottom length of the triangle.
- Height (h) — the perpendicular distance from the base to the top vertex.
- Square Units — units used to measure area, such as square inches, meters, feet, or yards.
Action Items / Next Steps
- Practice finding the area of triangles using the formula base × height ÷ 2.
- Remember to label answers with the correct square units.