Diagram of the adjacent picture frame has outer dimensions = 24 cm × 28 cm and inner dimensions 16 cm × 20 cm. Find the area of each section of the frame, if the width of each section is same.
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Solution
Given that, the width of each section is same. Therefore,
IB = BJ = CK = CL = DM = DN = AO = AP
IL = IB + BC + CL
28 = IB + 20 + CL
IB + CL = 28 cm − 20 cm = 8 cm
IB = CL = 4 cm
Hence, IB = BJ = CK = CL = DM = DN = AO = AP = 4 cm
Area of section BEFC = Area of section DGHA
=`[1/2 (20 + 28)(4)] cm^2 = 96 cm^2`
Area of section ABEH = Area of section CDGF
⇒Area of section ABEH = Area of section CDGF
= 1216+244=80 cm2
Concept: Area of a General Quadrilateral
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