Question

4. Draw the quadrilateral with vertices P(1,5), q(3,2), R(1-1) and S(-1,2) in a , Cartesian plane and join them in order , Also , name
the type of quadrilateral and find its area.​

Answer 1

Answer:

The quadrilateral formed is a parallelogram.

Let us see which particular quadrilateral is formed in the cartesian plane :

We know that, Distance Formula = √(x2-x1)²+(y2-y1)²

Distance PQ = √(3-1)²+(2-5)² = √4+9 = √13

Distance QR = √(1-3)²+(-1-2)² = √4+9 = √13

Distance RS = √(-1-1)²+(2-(-1))² = √4+9 = √13

Distance SP = √(1-(-1))²+(5-2)² = √4+9 = √13

Hence, It is a rhombus.

Area of a square is : a² = √13² = 13 unit².

(Refer the attachment)

Hence, the name of the quadrilateral is rhombus and the area is 13 unit².

More to know -

➸ What is a quadrilateral ?

It is a four sided closed figure. It has 4 edges and 4 vertices. It is a 2D shape.

➸ What is a square ?

A square is a quadrilateral with all sides equal and all angles 90.

➸ What is a parallelogram ?

A parallelogram is a quadrilateral with opposite sides parallel, opposite sides equal and the opposite angles equal.

➸ What is a rectangle ?

A rectangle is a quadrilateral with opposite sides equal and all angles 90.

➸ What is a kite ?

A kite is a quadrilateral with 2 pairs of adjacent sides equal.

➸ What is a rhombus ?

A rhombus is a quadrilateral with each side equal, opposite sides parallel to each other and all angles equal.