Question

Points T,U,V,W,X,Y lies on square
PQRS, as shown. If
PT = TU = UQ = QV =VW =WR = XS = SY
what fraction of the area of
square PQRS is shaded?​

Answer 1

Given : Points T,U,V,W,X,Y lies on square  PQRS

PT = TU = UQ = QV =VW =WR = XS = SY

To Find : what fraction of the area of  square PQRS is shaded

Solution:

Assume that Side of Square = 3

Area of Square = 3 x 3  = 9  sq unit

PT = TU = UQ = QV =VW =WR = XS = SY = 3/3 = 1

Area of larger triangle with TW vertices

= (1/2) * 2 * 2

= 2 sq units

Area of small triangles with bases TU & VW are

= (1/2) * 1 (1/2)

= 1/4

Hence Total Shaded area = 2 + 1/4 + 1/4

= 2 + 1/2

= 5/2

Fraction of the area of  square PQRS is shaded   = (5/2)/9

= 5/18

5/18 is correct answer,

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