Question

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

Answer 1

The outer dimensions of a picture frame = 28 cm × 24 cm

Length of the outer edge = 28 cm.

Breadth of the outer edge = 24 cm.

Dimensions of inner picture frame = 20 cm × 16 cm

Length of inner edge = 20 cm

Breadth of inner edge = 16 cm.

Area of ABC = 1/2 × b × h

= 1/2 × AC × BC

= 1/2 × 4 × 4 = 8 cm²

Area of rectangle CDEB = l × b

= CD × DE

= 20 × 4

= 80 cm²

Area of ADEF = 1/2 × b × h

= 1/2 × DF × DE

= 1/2 × 4 = 8sq.cm

∴ The area of the shaded region

= ar ΔABC + ar ▭ CDEB + ar ▭ ADEF

= 8 + 80 + 8

= 96 sq.cm.