FIND THE BASE AND HEIGHT OF A PARALLELOGRAM

Find the base or height of each parallelogram.

Problem 1 :

Solution :

Given, Area = 126 yd² and Base = 9 yd

Area of a parallelogram = Base x height

To find the height,

Height = Area / Base

Height = (126 yd²) / 9 yd

= 14 yd

So, the height of a parallelogram is 14 yd.

Problem 2 :

Solution :

Given, Area = 16 ft² and Height = 2 ft

Area = Base x Height

To find the base,

Base = Area / Height

Base = (16 ft²) / 2 ft

= 8 ft

So, the base of a parallelogram is 8 ft.

Problem 3 :

Solution :

Given, Area = 30 in² and Base = 3 in

Area = Base x height

To find the height,

Height = Area / Base

Height = (30 in²) / 3 in

= 10 in

So, the height of a parallelogram is 10 in.

Problem 4 :

Solution :

Given, Area = 44 ft² and Height = 11 ft

To find the base,

Base = Area / height

Base = (44 ft²) / 11 ft

= 4 ft

So, the base of a parallelogram is 4 ft.

Problem 5 :

Solution :

Given, Area = 160 in² and Base = 10 in

To find the height,

Height = Area / base

Height = (160 in²) / 10 in

= 16 in

So, the height of a parallelogram is 16 in.

Problem 6 :

Solution :

Given, Area = 65 yd² and Height = 5 yd 

To find the base,

Base = Area / height

Base = (65 yd²) / 5 yd

= 13 yd

So, the base of a parallelogram is 13 yd.

Problem 7 :

Solution :

Given, Area = 88 in² and Base = 8 in

To find the height,

Height = Area / base

Height = (88 in²) / 8 in

= 11 in

So, the height of a parallelogram is 11 in.

Problem 8 :

Solution :

Given, Area = 52 yd² and Height = 4 yd 

To find the base,

Base = Area / height

Base = (52 yd²) / 4 yd

= 13 yd

So, the base of a parallelogram is 13 yd.

Problem 9 :

Solution :

Given, Area = 105 ft² and Base = 7 ft

To find the height,

Height = Area / base

Height = (105 ft²) / 7 ft

= 15 ft

So, the height of a parallelogram is 15 ft.

Problem 10 :

The following parallelograms are drawn on centimetre-squared paper. Find the area of

Solution :

By observing the above parallelogram, the base = 4 units and height = 2 units

Area of parallelogram = base x height

= 4 x 2

= 8 square units.

Problem 11 :

A parallelogram has a base of 8 cm and a perpendicular height of 6 cm. Calculate the area of the parallelogram.

Solution :

Base = 8 cm and hegiht = 6 cm

Area of parallelogram = base x height

= 8 x 6

= 48 square cm

Problem 12 :

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

Solution :

Height of parallelogram = 30/2 ==> 15 cm

Area of shape = 2 (Area of parallelogram)

Base = 22 cm and height = 15 cm

= 2(22 x 15)

= 2(330)

= 660 square cm

Problem 13 :

Find x

Solution :

Area = 615 cm²

(2x + 7) 15 = 615

2x + 7 = 615/15

2x + 7 = 41

2x = 41 - 7

2x = 34

x = 34/2

x = 17 

So, the value of x is 17.

Problem 14 :

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

Solution :

Base of each parallelogram = (1/2) (7 - y)

Height = 18/2 ==> 9 cm

Area of the shape = 792

4(area of parallelogram) + area of middle part = 792

4(area of parallelogram) + area of middle part = 792

Area of middle part = 2(area of triangle)

2[1/2 x base x height]

= 7/2 x 9

= 3.5 x 9

= 31.5 cm²

4(area of parallelogram) + 31.5 = 792

4(area of parallelogram) = 792 - 31.5

= 760.5 cm²

So, the required area is 761 cm²

Problem 15 :

A parking lot is constructed in the shape of a parallelogram. What is the area of the parking lot?

Solution :

Area of parallelogram = base x height

= 200 x 120

= 24000 ft²

Problem 16 :

Sherice plays the bass in a garage band. Sherice’s parents let her and her friends use a section of their garage in the shape of a parallelogram for rehearsals. How much space in square feet does Sherice’s band have to practice in?

Solution :

Area of parallelogram = 10 x 6

= 60 square ft