Question

Find the perimeter and the area of the polygon with the given vertices.

A (12,2), B (12,13), C (15,13), D (15,2)
The perimeter is __ units.

The area is __ square units.

Answer 1

Solution :-

At first

Length of AB = 13 - 2 = 11 cm

Length of CD = 13 - 2 = 11 cm

Length of BC = 15 - 12 = 3 cm

Length of AD = 15 - 12 = 3 cm

Now

Perimeter = 11 + 11 + 3 + 3

Perimeter = 22 + 6

Perimeter = 28

Area = 11 × 33 = 33 cm

Answer 2

Explanation:

As points A and B have same x-coordinate, length of AB will be given by the difference of y-coordinate

AB = 13 - 2 = 11 units

As points C and D have same x-coordinate, length of CD will be given by the difference of y-coordinate

CD = 13 - 2 = 11 units

As points B and C have same y-coordinate, length of BC will be given by the difference of x-coordinate

BC = 15 - 12 = 3 units

As points A and D have same y-coordinate, length of AD will be given by the difference of x-coordinate

AD = 15- 12 = 3 units

AB = CD = 11 units

BC = AD = 3 units

So,ABCD is a rectangle

Area = 11 * 3 = 33 square units

Perimeter = 11+11+3+3 = 28 units