Class 7 Maths Perimeter and Area | Squares and Rectangles |

__Squares and Rectangles__

A square is a flat shape with 4 equal sides and every angle is a right angle i.e. 90°.

In the above figure, ABCD is a square.

Here AB = BC = CD = DA

Each interior angle is 90°.

The Perimeter of square is 4 times the side length. Let a be the length of each side of square.

Now, perimeter of square = 4 * a = 4a

Area of square = side length squared

= a * a

= a^{2}

**Problem: Find the area of a square park whose perimeter is 320 m.**

**Solution:**

Given: Perimeter of square park = 320 m

=> 4 * side = 320

=> side = 320/4 = 80 m

Now, Area of square park = side * side = 80 * 80 = 6400 m^{2}

Thus, the area of the square park is 6400 m^{2}.

A rectangle is a 4-sided flat shape with straight sides where all interior angles are right angles (90°).

Also opposite sides are parallel and of equal length.

In the above figure, ABCD is a rectangle where

AB = CD and BC = AD

Each interior angle is 90°.

Now, perimeter of a rectangle = 2(length + breadth)

Area of rectangle = length * breadth

**Problem: The length and breadth of a rectangular piece of land are 500 m and 300 m respectively.**

**Find: (i) Its area. (ii) The cost of the land, if 1 m ^{2} of the land costs Rs 10,000.**

**Solution:**

Given: Length of a rectangular piece of land = 500 m

and breadth of a rectangular piece of land = 300 m

(i) Area of a rectangular piece of land = Length * Breadth

= 500 * 300

= 1,50,000 m^{2}

(ii) Since, the cost of 1 m^{2} land = Rs 10,000

Therefore, the cost of 1,50,000 m^{2} land = 10,000 * 1,50,000 = Rs 1,50,00,00,000

**Triangles as Parts of Rectangles**

Let us take a rectangle and cut the rectangle along its diagonal to get two triangles as shown in the figure.

Superpose one triangle on the other. We find that sum of the areas of the two triangles is the same as the area of the rectangle. Both the triangles are equal in area.

Now, area of each triangle = (1/2) * (Area of the rectangle)

= (1/2) * (length of rectangle * breadth of rectangle)

Again take a square and divide it into four triangles as shown in the figure. The four triangles are equal in area.

Now, area of each triangle = (1/4) * (Area of the square)

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