Question

A polygon has vertices J(2,3), K(4,3), L(4,7) , and M(2,7) . What is the area of the polygon?

Answer 1

$\large\underline{\sf{Solution-}}$

Given coordinates are

Coordinates of J be (2, 3)

Coordinates of K (4, 3)

Coordinates of L (4, 7)

Coordinates of M (2, 7).

[ Please see the attachment ].

From graph we concluded that

JK = 2 units

KL = 4 units

LM = 2 units

MJ = 4 units

Also,

JK is perpendicular to KL.

KL is perpendicular to LM

LM is perpendicular to MJ

MJ is perpendicular to JK

It implies, JK = LM = 2units and KL = MJ = 4 units.

As we know that,

In a quadrilateral, if all the opposite pair of sides are equal and angle between the sides is 90°, then quadrilateral is a rectangle..

So, this figure, JKLM is a Rectangle.

Now, Area of rectangle JKLM= JK×KL = 4 × 2 = 8 sq. units.

Additional Information :-

Let's solve the same type of problem!!

Question :- A polygon has vertices A ( 2, 3), B (2, 1), C(0, 1) and D (0,3). Find the Perimeter of the polygon.

Solution:-

Given coordinates are

Coordinates of A be (2, 3)

Coordinates of B (2, 1)

Coordinates of C (0, 1)

Coordinates of D (0, 3).

[ Please see the attachment ].

From graph we concluded that

AB = 2 units

BC = 2 units

CD = 2 units

DA = 2 units

Also,

AB is perpendicular to BC.

BC is perpendicular to CD

CD is perpendicular to DA

DA is perpendicular to AB.

It implies, AB = BC = CD = DA = 2 units.

As we know that,

In a quadrilateral, if all the 4 sides are equal and angle between the sides is 90°, then quadrilateral is a square.

So, this figure, ABCD is a square.

Now, Perimeter of a square = 4 × side = 4 × 2 = 8 units.

Answer 2

Answer:

Step-by-step explanation:

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