Question

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.

Answer 1

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
$= (\frac{1}{2})×(28+20)×4$

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