SSC CGL Tier II 12 Jan 2017 Paper 1

Question : 56 of 100

Marks: +1, -0

In a trapezium ABCD, AB and DC are parallel sides and ∠ADC = 90°. If AB = 15 cm, CD = 40 cm and diagonal AC = 41 cm. then the area of the trapezium ABCD is

245 cm. $^{2}$
240 cm. $^{2}$
247.5 cm. $^{2}$
250 cm. $^{2}$

Validate

Solution:

(3)

∠ADC = 90°
AC = 41 cm.
CD = 40 cm.

∴ { AD } = √{ { AC } ^ { 2 } - { CD } ^ { 2 } }

=√ { 41 ^ { 2 } - 40 ^ { 2 } }

=√{ ( 41 + 40 ) ( 41 - 40 ) }

= √ { 81 } = 9 { cm }

∴ Area of trapezium ABCD

= { 1 }/ { 2 } ( { AB } + { CD } ) × { AD }

= { 1 } /{ 2 } ( 15 + 4 { 0 } ) × 9

=1/2 × 55 × 9 = 247.5

sq. cm.

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