Question 11
Question: Given a quadrilateral ABCD in which AB=7cm, BC=6cm, CD=5cm, AC=8cm and BD=9cm. Construct a triangle, equal in area to this quadrilateral on AB as base.
Answer: Steps of Construction:
Step 1:
Draw a rough sketch and mark in it the given measurements.
Step 2:
Construct quadrilateral ABCD with the given measurements.
Step 3:
Draw the diagonal BD.
Step 4:
Through C draw a line parallel to DB and intersecting AB produced at E.
Step 5:
Join DE.
Then, ADE is the required triangle.
Question 12
Question: 
Answer: Steps of Construction:
Draw a line l and on it cut off BC=5cm.
Produce YB to form a line YBY'.
Cut off BD'=2 cm on BY'.
Draw the perpendicular bisector of CD'. Let this bisector intersect BY at A.
Join AC.
Then ABC is the required triangle.
Question 13
Question: Construct D ABC in which BC=5cm, AB=5cm and the median BE=3cm.
Answer: Let ABC be the required triangle.
It is not possible to construct triangle ABC with only two side AB and BC known.
The other two triangles ABE and BEC also cannot be constructed with the given data.
Now E is the mid-point of AC.
If we draw a line DE through E and parallel to AB, then we know that 
Similarly D becomes the mid point of BC.
Steps of Construction:
Step 1:
We can construct D BDE with BD=2.5cm, BE=3cm and DE=2.5cm.
Step 2:
Produce BD to C such that DC=BD=2.5cm.
Step 3:
Join CE and produce it.
Step 4:
With B as centre and radius equal to 5cm, draw an arc meeting CE produced at A.
Step 5:
Join AB.
Then, ABC is the required triangle.
