Question

All the long sides of the shape below have the same length and each
long side is twice as long as each short side. If the perimeter of the figure is 160
cm. What is the area of the figure?

Answer 1

GiVeN : -

• Long sides are twice of short sides in length

• Perimeter of the figure = 160 cm

To FiNd : -

• Area of the figure

SoLuTiOn : -

• Let the shorter side be x cm

Then,

• Longer sides are 2x cm

In the given figure,

• Total number of Shorter sides = 8

• Total number of longer sides = 4

Then,

• Total length of all shorter sides = 8x

• Total length of all longer sides = 4×2x = 8x

Now,

• Perimeter of Figure is = 160

So,

=> 8x + 8x = 160

=> 16x = 160

=> x = 160/16 = 10 cm

Now,

• Longer side = 2x = 2× 10 = 20cm

• Shorter side = x = 10 cm

Now,

In the given figure,

We see it clearly there are 4 rectangles.which make the whole figure.

So,

• Area of figure = Area of 4 rectangles

So,

Area of Rectangle = l × b

Here,

• Length (l) = 20cm

• Breadth (b) = 10cm

=> Area of 4 rectangle = 4(20 × 10)

=> 4 × 200 = 800 cm^2

Then,

Area of figure = 800cm^2