Question

In the figure given below, find the area of shaded region: (All measurements are in cm)

Answer 1

The shaded region is a uniform-width frame (thickness 2 cm) around an inner 18 × 8 rectangle.

From the diagram:

• Outer top length = 20 cm

• Inner top length = 18 cm

So frame thickness =

`(20-18)/2` = 1 cm on each side

`(12-8)/2` = 2 cm thickness

Step 1: Outer Rectangle Area

Width = 18 + 2 + 2 = 22 cm

Height = 8 + 2 + 2 = 12 cm

Outer Area = 22 × 12

= 264 cm²

Step 2: Inner Rectangle Area

Inner Area = 18 × 8

= 144 cm²

Step 3: Shaded Area = Outer – Inner

Shaded Area = 264 − 144

= 120 cm²

But the shaded region is not the full frame, the bottom bar extends only 12 cm, not the full 22 cm width.

Missing bottom area:

Missing length = 22 − 12 = 10 cm

Frame thickness = 2 cm

Missing area = 10 × 2 = 20 cm²

120 − 20 = 100 cm²

Let’s incorporate the right side, which is only 2 cm tall, not full height.

Height missing = 12 − 2 = 10 cm

Thickness = 2 cm

Missing right area = 10 × 2 = 20 cm²

Now total missing area:

20 + 20 = 40 cm²

120 − 40 = 80 cm²

Missing bottom area:

6 × 2 = 12 cm²

Right missing:

(12 − 2) × 2 = 20

Total missing = 12 + 20 = 32

Correct shaded:

120 − 32 = 88

Top bar: 20 × 2 = 40

Left bar: 12 × 2 = 24

Bottom bar: 12 × 2 = 24

Total shaded: 40 + 24 + 24 = 88