4. In quadrilateral PQRS, PQ = 27 cm, QR = 30 cm,
RS = 52 cm, SP = 53 cm and PR = 51 cm, then
find its area.
Answers
Area of Quadrilateral PQRS = 1194 cm²
Step-by-step explanation:
In quadrilateral PQRS, PQ = 27 cm, QR = 30 cm,
RS = 52 cm, SP = 53 cm and PR = 51
Area of Quadrilateral PQRS = area of Δ PQR + Area of Δ PSR
area of Δ PQR
27 , 30 , 51
s = (27 + 30 + 51)/2 = 54
Area = √ 54 ( 54 - 27)(54 - 30)(54 - 51)
= √54 * 27 * 24 * 3
= √27 * 2 * 27 * 2 * 2 * 2 * 3 * 3
= 27 * 2 * 2 * 3
= 324 cm²
area of Δ PSR
52 , 53 , 51
s = (52 + 53 + 51)/2 = 78
Area = √ 78 ( 78 - 52)(78 - 53)(78 - 51)
= √78 * 26 * 25 * 27
= √26 * 3 * 26 * 5 * 5 * 3 * 3 * 3
= 26 * 3 * 3 * 5
= 1170 cm²
Area of Quadrilateral PQRS = 324 + 1170 = 1194 cm²
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