Find the area of the kite PQRS with P(5,0), Q(8,6), R(5,8) and S(2,6)?

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Find the area of the kite PQRS with P(5,0), Q(8,6), R(5,8) and S(2,6)?

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Answer 1 · 2016-01-10T17:13:03

$S_{Kite PQRS} = 24 s q . u n i t s$ $S_("Kite PQRS") = 24 sq. units$

Explanation:

Since the formula of a kite's area is
$S = (\frac{1}{2}) d 1 \cdot d 2$ $S=(1/2)d1*d2$
where
$d 1 = kite's long diagonal$ $d1="kite's long diagonal"$
$d 2 = kite's short diagonal$ $d2="kite's short diagonal"$
we need to know the length of the diagonals.

In the kite PQRS the diagonals are PR and QS:
$P R = \sqrt{{(5 - 5)}^{2} + {(8 - 0)}^{2}} = 8$ $PR=sqrt((5-5)^2+(8-0)^2)=8$
$Q S = \sqrt{{(2 - 8)}^{2} + {(6 - 6)}^{2}} = 6$ $QS=sqrt((2-8)^2+(6-6)^2)=6$

So
$S = (\frac{1}{2}) d 1 \cdot d 2 = (\frac{1}{2}) 8 \cdot 6 = 24$ $S=(1/2)d1*d2=(1/2)8*6=24$

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Find the area of the kite PQRS with P(5,0), Q(8,6), R(5,8) and S(2,6)?

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