Construct a quadrilateral PLAY , PL = 7cm, LA = 6cm, AY = 6cm, PA = 8cm, PY = 7cm and find its area
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Area of quadrilateral= Area of PLA+Area of ∆PAY.
Area of ∆ PLA
Using Heron's Formula.
S= a+b+c/2 [ a= 8cm,b= 7cm,c= 6cm where s= semi-perimeter]
S= 8+7+6/2
S= 21/2
S= 10.5
S= √s(s-a)(s-b)(s-c)
S= √10.5(10.5-8)(10.5-7)(10.5-6)
S= √10.5×2.5×3.5×4.5
S= √105/10×25/10×35/10×45/10
S= √105×25×35×45/10000
S= (3×7×5)×(5×5)×(5×7)×(5×3×3)/100
S= 3×7×5×5×√5×3
S= 525√15/100. [We know √15=3.872]
S= 525×3.872/100
S= 2032.8/100
S= 20.328
So, area of ∆PLA= 20.328cm².
Area of ∆PAY= ½×Base×Height
Area of ∆PAY=½×6×7
Area of ∆PAY= 3×7
Area of ∆PAY=21cm²
Area of quadrilateral= Area of PLA+Area of ∆PAY.
Area of quadrilateral= 20.328+21
Area of quadrilateral= 41.328
Step-by-step explanation:
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