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The base of a triangle is 14 cm and its height is 12 cm. Find the area of the triangle.
84 cm²
168 cm²
42 cm²
96 cm²
84 cm²
The area of a triangle is calculated using the standard geometric formula that relates its base and height. Given a base of 14 cm and a height of 12 cm, multiplying them together and dividing by two yields 84 cm².
The area of a triangle is calculated using the standard geometric formula that relates its base and height. Given a base of 14 cm and a height of 12 cm, multiplying them together and dividing by two yields 84 cm².
Imagine a rectangular piece of paper measuring 14 cm by 12 cm with an area of 168 cm². If you cut it diagonally from corner to corner, you get two identical triangles, each having half of the total area, which is 84 cm².
Area=21×b×h — Area of a triangle given base and height
The area formula of a triangle, Area=21×base×height, is derived from the area of a parallelogram. A parallelogram can be divided into two congruent triangles by its diagonal, meaning a single triangle's area is exactly half of the parallelogram formed by the same base and height.
The height must be perpendicular to the corresponding base.
The unit of area is always in square units, such as cm2.
Land surveying and plot measurement
Calculating surface areas in engineering and construction
Standard formula: Area=21×14×12=84 cm2.
Option B (168 cm²) represents the area of the full parallelogram before dividing by 2.
A is correct — The area of the triangle calculated using 21×base×height is 84 cm².
Always verify whether the given height is perpendicular to the selected base before applying the area formula in competitive exams.
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