ABCD is a rectangle. AB = 10 cm. BC = 8 cm. P, Q, R and S are points on the sides of the rectangle. BP = CQ = DR = AS = x cm. (a) Show that the area, A cm2 , of the quadrilateral PQRS is given by the formula A = 2x2 – 18x + 80
Answers
Given : ABCD is a rectangle. AB = 10 cm. BC = 8 cm. P, Q, R and S are points on the sides of the rectangle. BP = CQ = DR = AS = x cm
To Find : show that the area of quadrilateral PQRS is given by the formula A = 2x² – 18x + 80
Solution:
ABCD is a rectangle. AB = 10 cm. BC = 8 cm
AB = CD = 10 cm
BC = AD = 8 cm
BP = CQ = DR = AS = x
Hence Sides Left are 10-x , 8-x , 10-x , 8-x
Area of ABCD = 10 x 8 = 80 cm²
Area of PQRS = Area of ABCD - 4 right angle triangle formed
= 80 - ( (1/2)(10-x)x + (1/2)(8-x)x + (1/2)(10-x)x + (1/2)(8-x)x )
= 80 - ( (10 - x)x + (8 - x)x)
= 80 - ( 18 - 2x)x
= 80 - 18x + 2x²
= 2x² - 18x + 80
Area of PQRS = 2x² - 18x + 80
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