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.