Question

1. (i) Find the perimeter and area of a square whose one side is 6.5 cm long.
(ii) Find the area of a square whose perimeter is 124 cm.
(iii) Find the perimeter and diagonal of a square whose area is 64 cm?.
2. Find in hectares the area of a square-shaped field 14 km long.​

Answer 1

Solution:

1. (i) Given that ;

One side of square = 6.5 cm

We know that ;

• Perimeter of square = 4 * side

⇒ Perimeter = 4 * 6.5

⇒ Perimeter = 26 cm

Now, Area of square = (side)²

⇒ Area = (6.5)²

⇒ Area = 42.25 cm².

Hence, the perimeter of square is 26 cm and the area of square is 42.25 cm².

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(ii) Given that ;

Perimeter of square = 124 cm

⇒ 4 * Side = 124

⇒ Side = $\sf \dfrac{124}{4}$

⇒ Side = 31

Area of square = (side)²

⇒ Area = (31)²

⇒ Area = 961 cm²

Hence, the area of square is 961 cm².

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(iii) Given that ;

Area of square = 64 cm²

⇒ (Side)² = 64

⇒ Side = √64

⇒ Side = 8 cm

Perimeter of square = 4 * side

⇒ Perimeter = 4 * 8

⇒ Perimeter = 32 cm

Diagonal of square = √2 * side

⇒ Diagonal = √2 * 8

⇒ Diagonal = 8√2 cm

Hence, the perimeter of square is 32 cm and the diagonal of square is 8√2 cm.

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2. Given that;

Side of Square field = 14 km

⇒ Area of square shaped field = (side)²

⇒ Area = (14 * 14) km²

⇒ Area = 196 km²

We know that ;

• 1km² = 100 hectares

So, 196 km² = 19600 hectares.

Hence, the area is 19600 hectares.

Answer 2

Answer:

1.

I. Perimeter of square = 4 × side

⇒ Perimeter = 4 × 6.5

⇒ Perimeter = 26 cm

Now, Area of square = (side)²

⇒ Area = (6.5)²

⇒ Area = 42.25 cm²

II. Perimeter of square = 124 cm

⇒ 4 × Side = 124

⇒ Side = 124 / 4

⇒ Side = 31

Area of square = (side)²

⇒ Area = (31)²

⇒ Area = 961 cm²

III. Area of square = 64 cm²

⇒ (Side)² = 64

⇒ Side = √64

⇒ Side = 8 cm

Perimeter of square = 4 × side

⇒ Perimeter = 4 × 8

⇒ Perimeter = 32 cm

Diagonal of square = √2 × side

⇒ Diagonal = √2 × 8

⇒ Diagonal = 8√2 cm

2. Side of Square field = 14 km

⇒ Area of square shaped field = (side)²

⇒ Area = (14 × 14) km²

⇒ Area = 196 km²

We know that, 1 km² = 100 hectares

So,

196 km² = 19600 hectares.