Question 1: Find the area of the parallelogram whose:

(i) base and height

(ii) base and height

Answer:

(i) Area of a parallelogram

(ii) Area of a parallelogram

Question 2: The height of a parallelogram is one-third of its base. If the area of the parallelogram is , find the height and the base.

Answer:

Let the Height , Base

Area of a parallelogram

Therefore Height , Base

Question 3: is a parallelogram with and . If the distance between. its larger sides is , find

(i) the area of the parallelogram;

(ii) the distance between its shorter sides

Answer:

(i) Area of a parallelogram

(ii) Let the distance between the shorter sides

Therefore

Question 4: is a parallelogram having adjacent sides and . If its area is , find the distance between its longer sides and that between its shorter sides.

Answer:

Let the distance between the longer sides

Therefore

Let the distance between the shorter sides

Therefore

Question 5: In the adjoining figure, is a parallelogram in which and diagonal . Find

(i) the area of parallelogram ;

(ii) the distance between and ;

(iii) the distance between and .

Answer:

(i)

Area of triangle

Therefore Area of parallelogram

(ii) Let the distance between the longer sides

Therefore

(iii) Let the distance between the shorter sides

Therefore

Question 6: Find the area of a rhombus whose perimeter is and altitude is .

Answer:

Side of Rhombus

Area of a parallelogram

*Note: Rhombus is a special parallelogram where all sides are equal.*

Question 7: The area of a rhombus is and its altitude is . Find the perimeter of the rhombus.

Answer:

Side (or Base) of Rhombus

Perimeter of Rhombus

Question 8: The area of a rhombus is and its perimeter is . Find its altitude.

Answer:

Side of Rhombus

Area of a Rhombus:

Question 9: Find the area of rhombus whose diagonals are : (i) (ii)

Answer:

(i) Area of Rhombus

(ii) Area of Rhombus

Question 10: The area of a rhombus is . If one of the diagonals is long, find the length of the other diagonal.

Answer:

Diagonal

Question 11: Find the area of a rhombus, each side of which measures and one of whose diagonals is .

Answer:

Area of triangle

Therefore Area of parallelogram

Question 12: Find the area of a trapezium whose parallel sides are and and the distance between them is .

Answer:

Area of Trapezium

Question 13: Find the area of a trapezium whose parallel sides are and and the distance between them is .

Answer:

Area of Trapezium

Question 14: The lengths of parallel sides of a trapezium are in the ratio and the distance between them is . If the area of the trapezium is , find the Lengths of its parallel sides.

Answer:

Let the length of the parallel sides be and respectively.

Therefore

Area of Trapezium

Hence the length of the parallel sides be and respectively.

Question 15: The height of the trapezium of the area is . If one of the base is , find the other.

Answer:

Let the other base be

Area of Trapezium

Question 16: In the adjoining figure, is a trapezium in which parallel sides are and the non-parallel sides are and . Find the area of the trapezium.

Answer:

Let and let the distance between the parallel lines

Therefore

Hence

Therefore

Area of Trapezium

Question 17: The parallel sides of a trapezium are and . Its non-parallel sides are both equal, each being . Find the area of the trapezium.

Answer: Let and let the distance between the parallel lines

Therefore

Hence

Therefore

Area of Trapezium

Question 18: The area of a trapezium is and its height is . If one of the parallel sides is longer than the other by , find the two parallel sides.

Answer:

Let the length of the parallel sides be and respectively.

Therefore

Area of Trapezium

Hence the length of the parallel sides be and respectively.

Question 19: In the adjoining figure, is a rectangle in which and . Find the area of the shaded region .

Answer:

Area of Trapezium

Question 20: Find the area of the figure , given alongside, it being given that

Answer:

Area of

Area of Trapezium

Therefore total area

Question 21: Find the area of the shaded region in the figure given alongside.

Answer:

Area of top rectangle

Area of bottom rectangle

Area of Trapezium

Therefore total area

Question 22: Find the area of the shaded region given below:

Answer:

Area of the shaded region +

Question 23: Find the area of the figure , it being given that: , .

Answer:

Area of the shaded region +

Question 24: Find the area of the field , in which and , and

Answer:

Area of

Area of

Area of

Area of

Area of

Area of

Total area