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This guide explains how to calculate the area of triangle ABC with base BC measured in 'a' units and height AD in 'h' units. By dividing the height AD into two equal parts at point O and constructing triangles AEO and AOF, we demonstrate that the area of triangle ABC can be calculated using the properties of rectangles. The final area formula derived is ½ * a * h, where 'a' is the length of base BC and 'h' is the height, simplifying the understanding of geometric relationships in triangles.
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E F D A O h units B C a units • Consider a triangle ABC having BC = a units. • Draw the height AD= h units. • Draw a line EF, dividing the height AD in equal parts at O.
A E O F B C • Cut the upper triangles AEO & AOF.
E F D A E O F B C • Join the triangle AOF in the side of FC & triangle AEO in the side of BE.
h/2 units A G E O F H B C D a units • Now BCHG forms a rectangle having BC = a units & height = h/2 units.
h/2 units A G E O F H B C D a units • Area of the triangle = Area of the rectangle = length x breadth = BC x BG = BC x OD = ( a x h/2) sq. units = ½ a. h sq. units
