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प्रश्न
In the following figure, ABCD, it is given that BC || AD. BC = 10 cm, AD = 6 cm, AB = 5 cm and BE = 3 cm. Find the area of the figure ABCD.
बेरीज
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उत्तर
Given: BC || AD, BC = 10 cm, AD = 6 cm, AB = 5 cm, BE = 3 cm.
Step-wise calculation:
1. AE is the perpendicular distance (height) from A to BC.
In right triangle ABE,
`AE = sqrt(AB^2 − BE^2)`
= `sqrt(5^2 - 3^2)`
= `sqrt(25 - 9)`
= `sqrt(16)`
= 4 cm
2. Area of trapezoid ABCD
= `((BC + AD)/2 ) xx "height"`
= `((10 + 6)/2) xx 4`
= `(16/2) xx 4`
= 8 × 4
= 32 cm2
Area (ABCD) = 32 cm2.
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