☐ Pqrs is an Isosceles Trapezium L(Pq) = 7 Cm. Seg Pm ⊥ Seg Sr, L(Sm) = 3 Cm, Distance Between Two Parallel Sides is 4 Cm, Find the Area of ☐ Pqrs - SSC (English Medium) Class 8 - Mathematics
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☐ PQRS is an isosceles trapezium l(PQ) = 7 cm. seg PM ⊥ seg SR, l(SM) = 3 cm, Distance between two parallel sides is 4 cm, find the area of ☐ PQRS
Draw a perpendicular from Q to line MR. Where it meets the line MR name it point N.
MN = PQ = 7 cm
In Δ PMS,
PM² + SM² = PS²
⇒ 4² + 3² = PS²
⇒ PS² = 16 + 9 = 25
⇒ PS = 5cm
PQRS is an isosceles trapezium so, PS = QR = 5 cm
PM = QN = 4 cm
So, NR = SM = 3 cm
SR = SM + MN + NR = 3 + 7 + 3 = 13 cm
Area of trapezium PQRS = `1/2 xx` (sum of parallel sides) x height
=`1/2 xx` (7 + 13) x 4
= 40 cm²
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Solution ☐ Pqrs is an Isosceles Trapezium L(Pq) = 7 Cm. Seg Pm ⊥ Seg Sr, L(Sm) = 3 Cm, Distance Between Two Parallel Sides is 4 Cm, Find the Area of ☐ Pqrs Concept: Area of a Trapezium.