PRACTICE PROBLEMS ON FINDING AREA OF RHOMBUS

Find the Area of Rhombus Shown in the Following Figures

Problem 1 :

Solution

Problem 2 :

Solution

Problem 3 :

Find the area of a rhombus whose base is 14 cm and height is 9 cm.

Solution

Problem 4 :

Find the missing value. 

Solution

Problem 5 :

The area of a rhombus is 100 sq. cm and length of one of its diagonals is 8 cm. Find the length of the other diagonal.

Solution

Problem 6 :

A sweet is in the shape of rhombus whose diagonals are given as 4 cm and 5 cm. The surface of the sweet should be covered by an aluminum foil. Find the cost of aluminum foil used for 400 such sweets at the rate of $ 7 per 100  sq. cm.

Solution

Problem 7 :

If the area of a rhombus is 14504 m² and the ratio of diagonals is 37 : 49 then, find the length of the shorter diagonal.

Solution

Problem 8 :

If the diagonal of a rhombus of side 15 cm are in the ratio 3 : 4, find the area of rhombus.

a)  54 sq.cm     b)  108 sq.cm     c)  144 sq.cm

d) 200 sq.cm      e) None of these

Solution

Problem 1 :

If the lengths of the diagonals of a rhombus are  16 cm and 30 cm, find its area.

Solution

Problem 2 :

Find the area of the rhombus shown below. 

Solution

Problem 3 :

Area of a rhombus is 192 square cm. If the length of one of the diagonals is 16 cm, find the length of the other diagonal. 

Solution

Problem 4 :

Area of a rhombus is 120 square units. If the lengths of the diagonals are 10 units and (7x + 3) units, then find the value of x.  

Solution

Problem 5 :

Area of the rhombus shown below is 48 square inches. What is the value of x ? 

Solution

Problem 6 :

Find the area of the rhombus shown below.

Solution

Problem 7 :

Find the area of the rhombus having each side equal to 17 cm and one of its diagonals equal to 16 cm.

Solution

Problem 8 :

One of the diagonals of a rhombus is double and other diagonal. Its area is 25 sq.cm. The sum of the diagonal is :

a)  10 cm    b)  12 cm    c)  15 cm    d)  16 cm

Solution

Problem 9 :

The perimeter of the rhombus is 56 m, and its height is 5 m. Its area is 

a)  64 sq.m    b)  70 sq.m    c)  78 sq.m    d)  84 sq.m

Solution

Problem 10 :

The length of one diagonal of a rhombus is 80% of the other diagonal. The area of the rhombus is how many times the square of the length of other diagonal ?

a)  4/5    b)  2/5    c)  3/4    d)  1/4

Solution

Word Problems on Finding Area of Rhombus

Problem 1 :

Cedric is constructing a kite in the shape of a rhombus. The spars of the kite measure 15 inches and 24 inches. How much fabric will Cedric need for the kite ?

Solution

Problem 2 :

A kite in the shape of a rhombus has diagonals that are 25 inches long and 15 inches long. What is the area of the kite?

Solution

Problem 3 :

The diagonals of a rhombus are 12 in. and 16 in. long. The length of a side of the rhombus is 10 in. What is the height of the rhombus ?

Solution

Problem 4 :

The area of a rhombus is 150 cm². The length of one of its diagonals is 10 cm. The length of the other diagonal is :

a)  25 cm   b)  30 cm   c)  35 cm    d)  40 cm

Solution

Problem 5 :

If the diagonals of a rhombus are 24 cm and 10 cm, the area and perimeter of the rhombus are respectively,

a)  120 cm², 52 cm           b)  120 cm², 64 cm

c)  240 cm², 52 cm           d)  240 cm², 64 cm

Solution

Problem 6 :

Each side of the rhombus are 26 cm and one of its diagonals is 48 cm long. The area of rhombus is :

a) 240 cm²    b)  300 cm²     c)  360 cm²        d) 480 cm²

Solution

Problem 7 :

If the diagonals of a rhombus of side 15 cm are in the ratio 3 : 4, find the area of the rhombus.

a)  54 sq.cm     b)  108 sq.cm     c)  144 sq.cm

d)  216 sq.cm     e) none

Solution

Problem 8 :

PQRS is a rhombus perimeter is 32 cm and interior angle QRS = 120. What is the area of the rhombus PQRS ?

Solution

Find the Area of a Rhombus with Vertices

Problem 1 :

Find the area of a rhombus with the following vertices taken in order.

(1, 4), (5, 1), (1, -2), (-3, 1)

Solution

Problem 2 :

Find the area of a rhombus with the following vertices taken in order.

(3, 0), (4, 5), (-1, 4), (-2, -1)

Solution

Problem 3 :

Kite CHSR has vertices at C(0, 3), H(-4, 0) S (0, -7) and R(4, 0). Find the area of kite CHSR.

Solution

Problem 4 :

The area of rhombus is 84 sq.cm and the length of one diagonal is 24 cm. The length of the other diagonal is 

Solution

Problem 5 :

The diagonal of a quadrilateral are perpendicular bisectors of each other. If the length of one diagonal is 3 cm and the area of the quadrilateral is 180 cm², find the length of the other diagonal.

Solution

Problem 6 :

The length of one of the diagonals of a kite is 4 cm longer than twice the length of the other diagonal. The area of the kite is 15 cm². Find the length of each diagonal.

Solution

Problem 7 :

The length of one of the diagonals of a rhombus is 5 cm less than the length of the other diagonal. The area of the rhombus is 33 cm². Find the length of each diagonal.

Solution

Problem 8 :

Show that the points A(2, –1), B(3, 4), C(–2, 3) and D(–3, –2) forms a rhombus but not a square. Find the area of the rhombus also.

Solution

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.