Question

18. Find the perimeter, area and diagonal of a square each of whose sides measures.
16 cm
(ii) 8.5 m
(iii) 2.5 dm
19. The perimeter of a square is 28 cm. Find its area and the length of its diagonal.​

Answer 1

Solution :-

18. i.) Side of the square = 16 cm

$\star$ Perimeter of a square

= 4 x side

= 4 x 16 cm

= 64 cm

$\star$ Area of a square

= (side)²

= (16 cm)²

= 256 cm²

$\star$ Diagonal of a square

= $\sqrt{2}$ x side

= $\sqrt{2}$ x 16 cm

= 1.41 x 16 cm    [$\sqrt{2}$ = 1.41]

= 22.56 cm

ii.) Side of the square = 8.5 m

$\star$ Perimeter of a square

= 4 x side

= 4 x 8.5 m

= 34 m

$\star$ Area of a square

= (side)²

= (8.5 m)²

= 72.25 m²

$\star$ Diagonal of a square

= $\sqrt{2}$ x side

= $\sqrt{2}$ x 8.5 m

= 1.41 x 8.5 m    [$\sqrt{2}$ = 1.41]

= 11.985 m

iii.) Side of the square = 2.5 dm

$\star$ Perimeter of a square

= 4 x side

= 4 x 2.5 dm

= 10 dm

$\star$ Area of a square

= (side)²

= (2.5 dm)²

= 6.25 dm²

$\star$ Diagonal of a square

= $\sqrt{2}$ x side

= $\sqrt{2}$ x 2.5 dm

= 1.41 x 2.5 dm    [$\sqrt{2}$ = 1.41]

= 3.525 dm

19. Perimeter of a square = 28 cm

=> 4 x side = 28 cm

=> side = $\frac{28\:cm}{4}$

=> side = 7 cm

$\star$ Area of a square

= (side)²

= (7 cm)²

= 49 cm²

$\star$ Diagonal of a square

= $\sqrt{2}$ x side

= $\sqrt{2}$ x 7 cm

= 1.41 x 7 cm    [$\sqrt{2}$ = 1.41]

= 9.87 cm

More to Know:-

$\star$ Perimeter of rectangle = 2(Length + Breadth)

$\star$ Diagonal of rectangle = $\sqrt{(Length)^{2} +(Breadth)^{2}}$

$\star$ Area of rectangle = Length x Breadth

$\star$ Circumference of a circle = π x diameter

                         OR

  Circumference of a circle = 2 x π x radius

$\star$ Area of a circle = π x (radius)²