Question

Observe the shapes 1, 2, 3 and 4 in the figure. Which of the following statements is not correct?

• A. Shapes 1, 3 and 4 have different areas and different perimeters.
• B. Shapes 1 and 4 have the same area as well as the same perimeter.
• C. Shapes 1, 2 and 4 have the same area.
• D. Shapes 1, 3 and 4 have the same perimeter.

Answer 1

The correct option is A

Shapes 1, 3 and 4 have different areas and different perimeters.

Area of shape1 = $1+3+3+5+6$ = 18 (units)${}^2$

Area of shape2 $=6\times 3=18$ (units)${}^2$

Area of shape3 = $1+3+5+7=16$ (units)${}^2$

Area of shape4 = $2\times 9=18$ (units)${}^2$

So, the shapes 1, 2 and 4 have same area.

Perimeter of shape1 $=1+1+2+2+2+1+1+1+6+5=22$ units

Perimeter of shape2 $=6+3+6+3=18$ units

Perimeter of shape3 $=2\times (1+1+1+1+1+1+1)+7+1=14+7+1=22$ units

Perimeter of shape4 $=2\times (9+2)=2\times 11=22$ units

From the above, we can say that 1, 3 and 4 have the same perimeter and 1, 2 and 4 have the same area.