Overview
This lecture explains how to calculate the area of a triangle using the base and height, working through four sample problems.
Area of a Triangle Formula
- The area of a triangle is the amount of space inside its boundaries.
- Formula: Area = (base × height) ÷ 2.
- "Base" is any side of the triangle, and "height" is the perpendicular distance from the base to the opposite vertex.
- Placing two letters (like BH) together means multiplication.
Example Problems
- Example 1: Base = 5 inches, Height = 12 inches.
- 5 × 12 = 60, 60 ÷ 2 = 30, Area = 30 square inches.
- Reason for ÷ 2: A triangle is half of a rectangle or parallelogram, hence dividing by 2.
- Example 2: Base = 14 meters, Height = 5 meters.
- 14 × 5 = 70, 70 ÷ 2 = 35, Area = 35 square meters.
- Example 3: Base = 9 feet, Height = 3 feet.
- 9 × 3 = 27, 27 ÷ 2 = 13.5, Area = 13.5 square feet.
- Example 4: Base = 5 yards, Height = 6 yards (outside triangle is acceptable).
- 5 × 6 = 30, 30 ÷ 2 = 15, Area = 15 square yards.
Units in Area
- Always write area answers in square units (e.g., square inches, square meters).
Key Terms & Definitions
- Area — the space inside a 2D shape.
- Base — any one side of a triangle used for calculations.
- Height — the perpendicular distance from the base to the top vertex.
- Square units — units used to express area, such as in², m², ft², yd².
Action Items / Next Steps
- Practice using the area formula on different triangles with provided base and height values.
- Remember to label your answers with the correct square units.