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(C) The kite consists of a square $ABCD$ and an isosceles triangle at the bottom.Given that the diagonal of the square is $44 \, cm$.The area of a squ

Vedclass · Accepted Answer

$373.15$

Vedclass · Answer

(C) The kite consists of a square $ABCD$ and an isosceles triangle at the bottom.Given that the diagonal of the square is $44 \, cm$.The area of a square can be calculated using the diagonal $d$ as $	ext{Area} = \frac{1}{2} d^2$.$	ext{Area of square } ABCD = \frac{1}{2} 	imes 44 	imes 44 = 968 \, cm^2$.The square is divided into four equal triangles by its diagonals. Each triangle has an area of $\frac{968}{4} = 242 \, cm^2$.From the figure:- Red shade (part $IV$) $= 242 \, cm^2$.- Yellow shade (parts $I$ and $II$) $= 242 + 242 = 484 \, cm^2$.- Green shade (part $III$ and the bottom triangle).For the bottom triangle with sides $20 \, cm, 20 \, cm, 14 \, cm$:Semi-perimeter $s = \frac{20+20+14}{2} = 27 \, cm$.Area $= \sqrt{s(s-a)(s-b)(s-c)} = \sqrt{27(27-20)(27-20)(27-14)} = \sqrt{27 	imes 7 	imes 7 	imes 13} = 21 \sqrt{39} \approx 21 	imes 6.245 = 131.15 \, cm^2$.Total Green shade $= 242 + 131.15 = 373.15 \, cm^2$.

How much paper of each shade is needed to make a kite as shown in the figure,where $ABCD$ is a square with diagonal $44 \, cm$? (in $cm^2$)

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