Give a method to obtain a quadrilateral whose area is half that of a given quadrilateral. Class 8

Give a method to obtain a quadrilateral whose area is half that of a given quadrilateral. Class 8

Question 1.

Give a method to obtain a quadrilateral whose area is half that of a given quadrilateral. Class 8

Solution:

Let ABCD be a given quadrilateral. Join BD and draw AM and CN perpendiculars BD.

Now, find mid-point P of AM and mid-point Q of CN.

Then, join DP, PB, BQ and DQ.

Then, BPDQ is the required quadrilateral whose area is equal to half of area of quadrilateral ABCD.

Question 2.

Observe the parallelograms in the figure below. Class 8

(i) What can we say about the areas of all these parallelograms?

(ii) What can we say about their perimeters? Which figure appears to have the maximum perimeter, and which has the minimum perimeter?

Solution:

(i) Areas of all these parallelograms are equal.

(ii) Figure (g) appears to have maximum perimeter and figure (a) appears to have minimum perimeter.