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

Answer:

Area of a parallelogram

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

Answer:

Area of Rhombus

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

Answer:

Area of Rhombus

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

Therefore

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

Therefore

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

Therefore

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

Answer:

Perimeter of a Rhombus

Question 9: In a quadrilateral , diagonal and the lengths of the perpendicular from 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:

Area

Offsets are and

Diagonal

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:

Area

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.

Area

Therefore cost of land

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

Answer:

Area of trapezium

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

Therefore

Therefore Area of trapezium

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:

Area of trapezium

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

Therefore

Therefore Area of trapezium

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

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

Therefore sides are and

Therefore

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

Therefore

Let the height of the second parallelogram

Therefore

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:

Area

Therefore

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:

Area of the triangle

Therefore

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:

Cross-section area

Therefore