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Question

A trapezium whose parllel side are 25cm and 10cm and non parllel side are 14cm and 13cm find its area.

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Solution


Dear student, we can do this question by splitting the trapezium into a triangle (ADE in the figure) and a parallelogram (ABCE in the figure)
Now consider the triangle. Heron's formula for finding the area of a traingle is square root of s left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis end root
where s : semiperimeter = (14+15+13)/2 = 21

and a,b,c are the sides.
therefore the area is
square root of 21 cross times left parenthesis 21 minus 15 right parenthesis cross times left parenthesis 21 minus 14 right parenthesis cross times left parenthesis 21 minus 13 right parenthesis space end root = 84.
Area of the triangle is 84. Now find the area of the parallelogram. Area of parallelogram = base×height. Base of parallelogram is 10 cm. (From the figure base is 10 cm). Height of triangle ADE and the paralellogram is the same. Also we know the base and area of the triangle so we can find its height. Area is 84. base of triangle is 15 cm from the figure. So 84 space equals space 0.5 space cross times space 15 space cross times space h e i g h t left parenthesis 84 divided by 15 right parenthesis cross times 2 space equals space h e i g h t h e i g h t space equals space 11.2

height of triangle = height of parallelogram = 11.2
Area of parallelogram = 11.2 × 10 = 112.
Now total area of the trapezium = area of triangle + area of parallelogram = 84 + 112 = 196.

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