FINDING THE AREA OF PARALLELOGRAM

Find the area of each parallelogram.

Problem 1 :

Solution :

Base = 4 unit

Height = 3 unit

Area of parallelogram = base × height

= 4 × 3

= 12 units²

So, area of parallelogram is 12 units².

Problem 2 :

Solution :

Base = 6 unit

Height = 3 unit

Area of parallelogram = base × height

= 6 × 3

= 18 units²

So, the area of parallelogram is 18 units².

Problem 3 :

Solution :

Base = 7 ft

Height = 3 ft

Area of parallelogram = base × height

= 7 × 3

= 21 ft²

So, area of parallelogram is 21 ft².

Problem 4 :

Solution :

Base = 9 yd

Height = 7 yd

Area of parallelogram = base × height

= 9 × 7

= 63 yd²

So, area of parallelogram is 63 yd².

Problem 5 :

Solution :

Base = 5 cm

Height = 2 cm

Area of parallelogram = base × height

= 5 × 2

= 10 cm²

So, the area of parallelogram is 10 cm².

Problem 6 :

Solution :

Base = 10 yd

Height = 9 yd

Area of parallelogram = base × height

= 10 × 9

= 90 yd²

So, the area of parallelogram is 90 yd².

Problem 7 :

Find the base of a parallelogram with an area of 18 square inches and a height of 2 inches.

Solution :

Given, Area = 18 in²

Height = 2 in

Area of parallelogram = base × height

18 = base × 2

Base = 9 in

So, the base of parallelogram is 9 in.

Problem 8 :

Find the height of a parallelogram with an area of 63 square yards and a base 9 yards.

Solution :

Given, Area = 63 yd²

Base = 9 yd

Area of parallelogram = base × height

63 = 9 × height

Height = 7yd

So, the height of parallelogram is 7 yd.

Problem 9 :

Find the height of a parallelogram with an area of 41 square meters and base 8.2 meters.

Solution :

Given, Area = 41 m²

Base = 8.2 m

Area of parallelogram = base × height

41 = 8.2 × height

Height = 5 m

So, height of parallelogram is 5 m.

Problem 10 :

Find the area of the figure.

Solution :

Area of the field = Area of triangle + area of trapezium

Base of triangle = 7 ft and height = 8 ft

Let a and b be parallel sides of trapezium.

a = 6 ft and b = 6 + 7 ==> 13 ft, height of the trapezium = 8 ft

= (1/2) x base x height + (1/2) x h (a + b)

= (1/2) x 7 x 8 + (1/2) x 8 x (6 + 13)

= 28 + 4 x 19

= 28 + 76

= 104 square feet

Problem 11 :

The area of the parallelogram-shaped forest bordered by roads is 99,000 square yards. What is the length of the deer trail?

Solution :

Area of parallelogram = 99000 square feet

1 square yards = 9 square feet

1 square feet = 1/9 square yards

= 99000/9

= 11000 square yards

Base = 660 yards

base x height = 11000

660 x height = 11000

height = 11000/660

= 16.6 yards

So, the length of deer trail is 16.6 yards

Problem 12 :

The side of an office building in Hamburg, Germany, is in the shape of a parallelogram. The area of the side of the building is about 2150 square meters. What is the length x of the portion of the building that extends over the river?

Solution :

Area of building = 2150 square meters

base = (39 + x) m and height = 25 m

base x height = 2150

(39 + x) ⋅ 25 = 2150

39 + x = 2150/25

39 + x = 86

x = 86 - 39

x = 47

So, the missing length of the parallelogram is 47 m.

Problem 13 :

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 :

Area of photo prop = Area of parallelogram - area of square

base = 8 ft ==> 8 x 12 ==> 96 inches

height = 4 ft ==> 4 x 12 ==> 48 inches

= (96 x 48) - (10 x 10)

= 4608 - 100

= 4508 square inches

Problem 14 :

A galaxy contains a parallelogram-shaped dust field. The dust field has a base of 150 miles. The height is 14% of the base. What is the area of the dust field?

Solution :

Base = 150 miles

Height = 14% of 150

= 0.14 (150)

= 21 miles

Area of the dust field = 150 x 21

= 3150 square miles

So, the required area of dust field is 3150 square field.