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Question

Mathematics Question on Area of a Polygon

Diagram of the adjacent picture frame has outer dimensions = 24 cm x 28 cm and inner dimensions 16 cm x 20 cm. Find the area of each section of the frame, if the width of each section is same.
section of frame

Answer

section of the frame

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
=(12)×(28+20)×4= (\frac{1}{2})×(28+20)×4

=(12)×48×4=96 cm2= (\frac{1}{2})×48×4 = 96\ cm^2
Area of section ABEH = Area of section CDGF
Area of section ABEH = Area of section CDGF
= [12(16+24)(4)]=80 cm2