Question 1: Find the area of a parallelogram whose base is and the corresponding altitude is .

Answer:

Question 2: Find the area of a rhombus whose diagonals are and .

Answer:

Question 3: If the lengths of the diagonals of a rhombus are and . what is the area of the rhombus.

Answer:

Question 4: The area of a rhombus is . If one of the diagonals is long, find the Length of the other diagonal.

Answer:

Given area of a rhombus is

Question 5: The area of a parallelogram is . If its altitude is twice the corresponding base, determine the base and the altitude.

Answer:

Let Base

Therefore Altitude

Hence

Therefore Base and Altitude

Question 6: The adjacent sides of a parallelogram are and . If the distance between the longer sides is , find the distance between the shorter sides.

Answer:

Let the distance between the shorter sides

Question 7: The area of a triangle is equal to the area of a parallelogram whose base is and altitude . If the base of the triangle is , find its altitude.

Answer:

Dimension of the triangle: Base , Height

Dimensions of the parallelogram: Base , Height

Question 8: The diagonals of a rhombus are and long. Find its perimeter.

Answer:

Perimeter of a Rhombus

Question 9: In a quadrilateral and the lengths of the perpendicular fro\text{ m } and no are and respectively. Find the area of the quadrilateral.

Answer:

Area of Area of + Area of

Question 10: Find the diagonal of a quadrilateral whose area is and whose offsets are and .

Answer:

Offsets are and

Question 11: Find the cost of levelling a plot of ground in the form of a quadrilateral at per square meter whose diagonal measure and its offsets and respectively.

Answer:

Therefore Cost of leveling

Question 12: Find the area of a quadrangular field whose diagonals measure and and bisect each other at right-angles. Find also the cost of land at the rate of per square meter.

Answer:

This is a rhombus since the diagonals are perpendicular to each other.

Therefore cost of land

Question 13: The parallel sides of a trapezium are and and its altitude is . Find its area.

Answer:

Question 14: Two parallel sides of a trapezium are and and other sides are and . Find the area of the trapezium.

Answer:

Area of the

Question 15: The cross-section of a canal is a trapezium in shape. If the canal is wide at the top, wide at the bottom and the area of the cross-section is , find the depth of the canal.

Answer:

Question 16: The parallel sides and of a trapezium are and respectively. If the sides and are and respectively. Find the distance between parallel sides and the area of trapezium ABCD.

Answer:

Area of the

Question 17: The area of a trapezium is . If the ratio of parallel sides is and the distance between them is , find the lengths of parallel sides.

Answer:

Let the sides be and

Therefore sides are and

Question 18: The parallel sides of an isosceles trapezium are in the ratio . If its height is and area is , find the perimeter.

Answer:

Let the sides be and

Therefore sides are and

Also

Therefore Perimeter

Question 19: The area of a parallelogram is and its height is . A second parallel gram has equal area but its base is more than that of the first. Obtain an expression in terms of and for the height of the parallelogram.

Answer:

Let the base of the first parallelogram

Let the height of the second parallelogram

Question 20: The area of a parallelogram is . If one altitude is half the corresponding base, determine the base and altitude of the parallelogram.

Answer:

Hence Base and Height

Question 21: A triangle and a parallelogram have the same base and same area. If the sides of the triangle are and , and the parallelogram stands on the base , find the height of the parallelogram.

Answer:

Question 22: The cross-section of a canal is in the form of a trapezium whose parallel sides are along the top and bottom of the canal. If the canal is wide at the top and wide at the bottom and the area of the cross-section is , find its depth.

Answer: