Question

Construct a quadrilateral ABCD, given that BC = 4.5cm. AO = 5.5 cm and CD = 5cm, the diagonal AC = 5.5cm and the other diagonal BD = 7cm.

Answer 1

Hint: Draw diagonal AC = 5.5cm first. Now take AD = 5.5cm and CD = 5cm as radius and A and C as the center, cut on the arc below AC and join them. Now take BC = 4.5cm and BD = 7cm. Take C and D as the center and cut an arc above AC to get point B. Join all the sides.

Complete step-by-step answer:

We have to construct a quadrilateral ABCD. We have been given the length of the sides and the diagonals of the quadrilateral.
We have been given 3 sides, BC = 4.5cm, AD = 5.5cm and CD = 5cm.

The diagonals are AC = 5.5cm and BD = 7cm.
First let us draw a rough figure with the given length of sides and diagonals. The figure shows the rough quadrilateral ABCD.
So, before we construct quadrilateral ABCD, let us check the steps which you have followed while constructing the quadrilateral.
Let us first draw a diagonal AC of length 5.5cm. Now let us first find point D. Take 5.5cm in a compass, take it as the radius and A as the center, draw an arc on the bottom of AC. Mark the point as D, where the two arcs intersect at bottom of AC. Thus join AD and CD.
Now let us find point B, take 4.5cm as radius and C as center, draw an arc on top of AC. Now take 7cm as radius and D as center, draw an arc on top of AC. Mark point as B, where the two arcs intersect at the top of AC. Now join BC and AB. Join BD to get the diagonal.
Now these are the steps of construction. With these steps in mind let us construct quadrilateral ABCD.
Hence, we have drawn the quadrilateral ABCD. Make all the sides and diagonals. By measuring the length of AB, we get the \[{{4}^{th}}\] side of the quadrilateral.

We got AB = 3cm.
Hence, we have constructed the quadrilateral ABCD.

Note: It is not necessary that you take diagonal AC as the base. You can also take diagonal BD first. But it is easier to take AC. In a construction like this you can’t start with the sides but you can start only with the diagonals, remember that.