Question

Draw a quadrilateral with measures as given below:

Draw a triangle of equal are and compute its area.

Answer 1

The given quadrilateral can be drawn using the following steps of construction:

1) Draw a line segment AB of length 5 cm.

2) Draw ∠XAB of measure 80° at point A.

3) Taking A as the centre and 3 cm as the radius, draw an arc which intersects ray AX at point D.

4) Draw ∠YDA of measure 120° at point D.

5) Taking D as the centre and 4 cm as the radius, draw an arc which intersects ray DY at point C.

6) Join 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) Join diagonal BD of the quadrilateral ABCD. 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.