in figure 11.23, PQ|| ,SP is perpendicular to PQ, PQ=60cm, SR=36cm and QR=25cm.Find the area of quadrilateral PQRS.
Answers
Answer:
336 cm²
Step-by-step explanation:
Let us draw a perpendicular from R to PQ. Name that point T. As PQ is parallel to SP so PT =36cm
Given - SR=36cm, PQ=60cm, RQ=25cm, TQ=24cm
By Pythagoras theorem in ∆RTQ,
25² = RT² + 24²
RT² = 25²-24²= 625 -576 = 49
RT=7cm
Area of trapezium= (36+60)7/2
=96*7/2
=48*7 = 336 cm²
Area Of Quadrilateral PQRS = 336 cm²
Step-by-step explanation:
GIVEN
SP = 36 cm
PQ = 60 cm
QR = 25 cm
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TO FIND
Area Of Quadrilateral PQRS
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We know that,
Hypotenuse² = Base² + Height²
Here,
Hypotenuse = QR = 25
Base = QT = PQ - SR = 60 - 36 = 24 cm
Height = ?
We know that,
Hypotenuse² = Base² + Height²
25² = 24² + Height²
Height² = 25² - 24²
Height² = 625 - 576
Height² = 49
Height = √49
Height = 7
Height = 7 cm
RT = 7 cm
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AREA OF RECTANGLE
We know that,
Area Of Rectangle = Length × Breadth
Here,
Length = 36 cm
Breadth = 7 cm
We know that,
Area Of Rectangle = Length × Breadth
Area Of Rectangle = 36 × 7
Area Of Rectangle = 252
Area Of Rectangle = 252 cm²
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AREA OF TRIANGLE
We know that,
Area Of Triangle = ½ × Base × Height
Here,
Base = 24 cm
Height = 7 cm
We know that,
Area Of Triangle = ½ × Base × Height
Area Of Triangle = ½ × 24 × 7
Area Of Triangle = ½ × 168
Area Of Triangle = 84
Area Of Triangle = 84 cm²
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AREA OF QUADRILATERAL PQRS
We know that,
Area Of Quadrilateral PQRS = Area Of Rectangle + Area Of Triangle
Area Of Quadrilateral PQRS = 252 + 84
Area Of Quadrilateral PQRS = 336
Area Of Quadrilateral PQRS = 336 cm²
