Question 1: In the given figure, is right angled at
in which
and
. Find the area of acute angled
, it being given that
Answer:
(since
is a right angled triangle)
Area of
Question 2: In the adjoining figure, area
Answer:
Area of
This is because are between the same parallels and have the same base.
Also, since are on the same base and between the same parallels, so the
Area of
Question 3: In the adjoining figure, area Find
Answer:
Also, since are on the same base and between the same parallels, so the
Area of
Area of
This is because are between the same parallels and have the same base.
Question 4: In trapezium , it is being given that
and diagonals
intersect at O. Prove that:
Answer:
Since are on the same base and between the same parallels, the area of the two
‘s will be equal.
Also Since are on the same base and between the same parallels,the area of the
‘s will be equal.
Now, subtract the area of from both sides we get
Question 5: In the adjoining figure, is a parallelogram,
is a point on
. Prove that :
are equal in area
Answer:
Since are on the same base and between the same parallels, so the
Area of
Similarly, are on the same base and between the same parallels, so the
Area of
Area
Hence Proved.
Question 6: In the adjoining figure, is a quadrilateral. A line through
, parallel to
, meets
produced in
. Prove that
.
Answer:
Similary,
Hence
But
Hence Proved that
Question 7: is any quadrilateral. Line segments passing through the vertices are drawn parallel to the diagonals of this quadrilateral so as to obtain a parallelogram
as shown in the adjoining figure. Prove that:
Answer:
Since
Hence Proven.