**Example 1 :**

Find the area of the figure given below.

**Solution :**

By observing the figure, it is a triangle.

Then, AC = base and BD = height

There are 4 units for the base and 3 units for height.

Finding the area :

Area of a triangle = 1/2 × base × height

= 1/2 × 4 × 3

Area = 6 sq.units

**Example 2 :**

Find the area and perimeter of the figure given below.

**Solution :**

By observing the figure, it is a square.

Then, HG = GF = EF = EH = side

There are 5 units for the side.

Finding the area :

Area of a square = side^{2}

= 5^{2}

Area = 25 sq.units

Finding the Perimeter :

Perimeter of a square = 4a

= 4(5)

Perimeter = 20 units

**Example 3 :**

**Solution :**

By observing the figure, it is a circle.

Then, OA = radius

There are 2 units for radius.

Finding the area :

Area of a circle = πr^{2}

= π(2^{2})

= 4π

Area = 4π sq.units

Draw the figure in a coordinate plane and find its area and perimeter.

**Example 4 :**

Triangle defined by A(3, 4), B(7, 4), and C(5, 7)

**Solution :**

By plotting the given points on the graph, we get

Now, there is a triangle.

Then, AB = base and CD = height

There are 4 units for the base and 3 units for height.

Finding the area :

Area of a triangle = 1/2 × base × height

= 1/2 × 4 × 3

Area = 6 sq.units

**Example 5 :**

Triangle defined by R(-2, -3), S(6, -3), and T(5, 4)

**Solution :**

By plotting the given points on the graph, we get

Now, there is a triangle.

Then, RS = base and TQ = height

There are 8 units for the base and 7 units for height.

Finding the area :

Area of a triangle = 1/2 × base × height

= 1/2 × 8 × 7

Area = 28 sq.units

**Example 6 :**

Rectangle defined by L(-2, -4), M(-2, 1), N(7, 1) and P(7, -4)

**Solution :**

By plotting the given points on the graph, we get

Now, there is a rectangle.

Then, LP = length and NP = width

There are 9 units for the length and 5 units for width.

Finding the area :

Area of a rectangle = length × width

= 9 × 5

Area = 45 sq.units

Finding the perimeter :

Perimeter of a rectangle = 2(length + width)

= 2(9 + 5)

= 2(14)

Perimeter = 28 units

**Example 7 :**

Square defined by W(5, 0), X(0, 5), Y(-5, 0) and Z(0, -5)

**Solution :**

By plotting the given points on the graph, we get

Now, there is a square.

But, we couldn’t calculate XY = YZ (side)

So, we are using the diagonals.

Here, d = 10 units

Finding the area :

Area of square using diagonals = 1/2
× d^{2}

= 1/2
× 10^{2}

= 1/2 × 100

Area = 50 sq.units

Finding the perimeter :

Perimeter of a square using diagonals = 4 ×
√(d^{2}/2)

= 4 ×
√(10^{2}/2)

= 4 × √100/2

= 4 × √50

= 4 × 5√2

= 20√2

Perimeter = 20√2 units

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