Question

Draw the quadrilateral ABCD with AB = 8.5 cm, BC = 4.5 cm, CD = 5 cm, DA = 6 cm, BD = 7.5 cm. Compute its area by drawing a triangle of equal area.

Answer 1

The measures of the sides of the quadrilateral to be constructed are AB = 8.5 cm, BC = 4.5 cm, CD = 5 cm, DA = 6 cm and BD = 7.5 cm.

The steps of construction are as follows:

1) Draw a line segment AB of length 8.5 cm.

2) Taking A as the centre and 6 cm as the radius, draw an arc on the upper side of line segment AB.

3) Taking B as the centre and 7.5 cm as the radius, draw an arc intersecting the previously drawn arc at point D.

4) Join AD and BD.

5) Taking D as the centre and 5 cm as the radius, draw an arc on the right side of point D.

6) Taking B as the centre and 4.5 cm as the radius, draw an arc intersecting the previously drawn arc at point C.

7) Join DC and BC.

Quadrilateral ABCD is the required quadrilateral.

We know that triangles lying on the same base and between the same parallels are equal in area.

Here, we need to construct a triangle whose area is equal to the area of the quadrilateral ABCD.

The steps of construction are as follows:

1) Draw a line l that is parallel to diagonal BD and passes through point C.

2) Extend line segment AB such that it touches line l at point E.

3) Join DE.

ΔADE is the required triangle whose area is equal to the area of the quadrilateral ABCD.

Disclaimer: The given dimensions are not sufficient to compute the area of the given quadrilateral by using the methods of finding area taught till your grade.