PRACTICE PROBLEMS ON FINDING AREA OF PARALLELOGRAM

Find the Area and Perimeter of the following Parallelograms 

Problem 1 :

Solution

Problem 2 :

Solution

Problem 3 :

Find the missing values.

Solution

Problem 4 :

Suresh won a parallelogram – shaped trophy in a state level chess tournament. He knows that the area of the trophy is 735 sq. cm and its base is 21 cm. what is the height of that trophy?

Solution

Problem 5 :

Janaki has a piece of fabric in the shape of a parallelogram. Its height is 12 m and its base is 18 m. She cuts the fabric into four equal parallelograms by cutting the parallel sides through its mid – points. Find the area of each new parallelogram.

Solution

Problem 6 :

A ground is in the shape of parallelogram. The height of the parallelogram is 14 meters and the corresponding base is 8 meters longer than its height. Find the cost of levelling the ground at the rate of $ 15 per sq. m.

Solution

Problem 7 :

The logo below is created by joining two congruent parallelograms. Calculate the area of the logo. 

Solution

Problem 8 :

Find x .

Solution

Problem 9 :

A shape is made from 4 congruent parallelograms. The area of the shape is 792cm²

Problem 10 :

If three consecutive vertices of a parallelogram ABCD are A(1, -2), B(3, 6) and C (5, 10), find its fourth vertex D.

Problem 1 :

Solution

Problem 2 :

Solution

Problem 3 :

A mirror is made of two congruent parallelograms as shown in the diagram. The parallelograms have a combined area of 9 1/3 square yards. The height of each parallelogram is 1 1/3 yards. How long is the base of each parallelogram ?

Solution

Problem 4 :

Find the base of a parallelogram if its area is 40 square cm and its altitude is 15 cm.

Solution

Problem 5 :

Find the area of the shape shown below. 

Solution

Problem 6 :

If the area of the shape shown below is 60 square inches, then find the value of x. 

Solution

Problem 7 :

You make a photo prop for a school fair. You cut a 10-inch square out of a parallelogram-shaped piece of wood. What is the area of the photo prop?

Solution

Problem 8 :

The area of a parallelogram can be expressed as the binomial 2x² − 10x. Which of the following could be the length of the base and the height of the parallelogram?

a. 2x(x² − 5x)             b. 2x(x − 5) 

c. (2x − 1)(x − 10)           d. (2x − 5)(x + 2)

Solution

Problem 9 :

The perimeter of the parallelogram below is 32 cm. What is the length of the longer side?

a. 9 cm      b. 10 cm      c. 6 cm     d. 12 cm

Solution

Problem 10 :

Find the area of the shaded region. You cut a 12-inch square out of the piece of wood. What is the area of the photo prop?

Solution

Problem 1 :

Find the area of the unshaded region.

Solution

Problem 2 :

Find the area of a quadrilateral ABCD whose sides are AB = 13cm, BC = 12cm, CD = 9cm, AD = 14cm and diagonal BD = 15cm.

Solution

Problem 3 :

A park is in the shape of a quadrilateral. The sides of the park are 15 m, 20 m, 26 m and 17 m and the angle between the first two sides is a right angle. Find the area of the park.

Solution

Problem 4 :

The front of an A-frame house is in the shape of a triangle. The height of the house is 20 feet. The area of the front of the A-frame is 600 square feet. Write and solve an equation to find the base of the A-frame house.

Solution

Problem 5 :

One side of a parallelogram is 18 cm and its distance from the opposite side is 8 cm. The area of the parallelogram

Solution

Problem 6 :

A parallelogram has sides 30 m and 14 m and one of its diagonals is 40 m long. then the area is :

Solution

Problem 7 :

A triangle and parallelogram are constructed on the same base such that their areas are equal. If the altitude of the parallelogram is 100 m, then the altitude of the triangle is 

a)  10√2 m     b)  100 m     c)  100√2 m      d)  200 m

Solution

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