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Area of Triangle — Standard Formula

The area of a triangle is half the product of a chosen base and its corresponding height.

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Student-friendly explanation

Any side of a triangle can be treated as base, but the height must be perpendicular to that base. The formula works for right, acute, and obtuse triangles when the correct height is used.

How to write this in exams

  1. 1

    Start with the exact idea

    The area of a triangle is half the product of a chosen base and its corresponding height.

  2. 2

    Then show how to use it

    Choose the base, identify its perpendicular height, substitute in 1/2 × base × height, simplify, and write square units.

  3. 3

    Add one concrete example

    If base = 12 cm and height = 5 cm, area = 1/2 × 12 × 5 = 30 cm².

  4. 4

    Avoid this incomplete answer

    80 cm² for base 10 cm and height 8 cm is wrong because the factor 1/2 is missed.

Definition

The area of a triangle is half the product of a chosen base and its corresponding height.

Example

If base = 12 cm and height = 5 cm, area = 1/2 × 12 × 5 = 30 cm².

Rule to remember

Area = 1/2 × base × height. The height must be perpendicular to the selected base.

Memory hook

Triangle area is half of the matching rectangle or parallelogram.

Examples and method

Worked example

A triangle has base 10 cm and height 8 cm. Area = 1/2 × 10 × 8 = 40 cm².

Method to apply

Choose the base, identify its perpendicular height, substitute in 1/2 × base × height, simplify, and write square units.

Diagram support

A triangle with base marked and perpendicular height drawn helps avoid using a slant side as height.

How CBSE asks it

Questions may give a diagram with an outside height, a right triangle, or a missing height from area and base.

Avoid common mistakes

Common confusion

Students sometimes use a slant side as height even when it is not perpendicular to the base.

Common wrong answer

80 cm² for base 10 cm and height 8 cm is wrong because the factor 1/2 is missed.

Exam tip

Look for the right-angle mark or perpendicular height before substituting values.

Quick check

A triangle has base 16 cm and perpendicular height 9 cm. What is its area?

The area is 1/2 × 16 × 9 = 72 cm² because the height is perpendicular to the chosen base.

Answer writing and exam use

1-mark answer

The area of a triangle is half the product of a chosen base and its corresponding height.

2-mark answer

The area of a triangle is half the product of a chosen base and its corresponding height. Area = 1/2 × base × height. The height must be perpendicular to the selected base. If base = 12 cm and height = 5 cm, area = 1/2 × 12 × 5 = 30 cm².

3-mark answer

Any side of a triangle can be treated as base, but the height must be perpendicular to that base. The formula works for right, acute, and obtuse triangles when the correct height is used. Area = 1/2 × base × height. The height must be perpendicular to the selected base. A triangle has base 10 cm and height 8 cm. Area = 1/2 × 10 × 8 = 40 cm². Questions may give a diagram with an outside height, a right triangle, or a missing height from area and base. 80 cm² for base 10 cm and height 8 cm is wrong because the factor 1/2 is missed.
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