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Find the area of the trapezium ABCD in which AB//DC, AB = 18 cm, ∠B = ∠C = 90°, CD = 12 cm and AD = 10 cm.

Area Trapezium Polygon

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Answer

Given:

AB = 18 cm

∠B = ∠C = 90°

CD = 12 cm

AD = 10 cm

Draw DL perpendicular to AB.

Find the area of the trapezium ABCD in which AB//DC, AB = 18 cm, ∠B = ∠C = 90°, CD = 12 cm and AD = 10 cm. Area of a Trapezium and a Polygon, Concise Mathematics Solutions ICSE Class 8.

Since, AL = AB - DC

= 18 - 12

= 6 cm

Also, DL = BC (Both are perpendiculars)

Using pythagoras theorem,

AD2 = AL2 + LD2

⇒ 102 = 62 + LD2

⇒ 100 = 36 + LD2

⇒ LD2 = 100 - 36

⇒ LD2 = 64

⇒ LD = 64\sqrt{64}

⇒ LD = 8 cm

As we know, the area of a trapezium = 12\dfrac{1}{2} (sum of parallel sides) x distance betweem the parallel sides.

= 12\dfrac{1}{2} (18 + 12) x 8

= 12\dfrac{1}{2} x 30 x 8

= 12\dfrac{1}{2} x 240

= 120 cm2

Hence, the area of the trapezium is 120 cm2.

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