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Answers
first construct the quadrilateral using the dimensions given. since, all the sides are given, it is rather easier to draw the quadrilateral. follow following steps
1. draw horizontal line segment of 8 cm
2. use compass amd make an arc of 6 cm from left of the 8 cm line segment.
3. using the compass, make an arc of 7 cm from righmost of 8 cm line segment. this arc should cut 6 cm arc drawn at step 2
4 join the point of intersection with both ends of 8 cm line segment.
5.again from the righ side of 8 cm line segment, make an arc of 4 cm length.
6. from the joining point of 6 cm and 7 cm arc, make an arc of 5 cm towards right so that it cuts the 4 cm arc
7. join the point of intersection to the points from where arcs were drawn.
8. the quadrilateral is complete.
9 . Now, to draw a triangle of equal area, we will have to draw a line which is parallel to the diagonal of 7 cm. the line may be drawn either from left bottom or from right top of quadrilateral.
10. to draw parallel line, we need to make an equal corresponding angle at the chosen point. (I am not telling the steps here)
11 suppose, we have drawn the parallel line from top right point of quadrilateral.
12. produce the 8 cm base towards right where it meets the parallel line
13. join the meetimg point with top left of the quadrilateral.
14. our desired triangle is with base 8 cm produced to point where it met parallel line, left side of 6 cm and third side from top left to right of base.
(The idea behind equal area is that the triangles made on same base and between same parallel lines have equal area.)