HOW TO FIND THE AREA OF A QUADRILATERAL

Find the area of each Parallelogram .

Problem 1 :

Solution :

By observing the figure, 

Base (b) = 16 ft and Height (h) = 18 ft

Area of a Parallelogram A = b × h sq. units.

= 16 ×18

Area = 288 ft²

Problem 2 :

Solution :

By observing the figure, 

Base (b) = 9 m and Height (h) = 5 m

Area of a Parallelogram  A = b × h sq. units.

= 8 × 9

Area = 72 m²

Find the area of each trapezoid .

Problem 3 :

Solution :

By observing the figure,

Base (b₁) = 12 in, Base (b₂) = 5 in and Height (h) = 4 in.

Area of a trapezoid A = 1/2 (b₁ + b₂) × h

= 1/2 (12 in + 5 in) × 4 in

= 1/2 (17 in) × 4 in

Area = 34 in²

Problem 4 :

Solution :

By observing the figure,

Base (b₁) = 6 ft, Base (b₂) = 2 ft, and Height (h) = 2 ft

Area of a trapezoid A = 1/2 (b₁ + b₂) × h

= 1/2 (6 + 2) × 2

= 1/2 (8) × 2

Area = 8 ft²

Find the area of each rhombus.

Problem 5 :

Solution :

By observing the figure,

Diagonal (d₁) = 6 cm and Diagonal (d₂) = 9 cm

Area of a rhombus A = 1/2 (d₁ × d₂) 

= 1/2 (6 × 9)

= 1/2 (54)

= 27 cm²

Problem 6 :

Solution :

By observing the figure,

Diagonal (d₁) = 12 in. and Diagonal (d₂) = 18 in.

Area of a rhombus A = 1/2 (d₁ × d₂) 

= 1/2 (12 in × 18 in)

= 1/2 (216 in²)

Area = 108 in²

Problem 7 :

A desktop in the shape of a parallelogram has a base of 30 inches and a height of 40 inches. What is the area of the desktop?

Solution :

Given,

Base of the desktop (b) = 30 in

Height of the desktop (h) = 40 in

To find the area of the desktop,

Area of a Parallelogram A = b × h

= 30 × 40

= 1200 in²

So, the area of the desktop = 1200 in²

Problem 8 :

A rhombus has one diagonal that is 14 centimetres long and one diagonal that is 12 centimetres long. What is the area of the rhombus?

Solution :

Given,

Diagonal (d₁) = 14 cm and Diagonal (d₂) = 12 cm

Area of a rhombus A = 1/2 (d₁ × d₂) 

= 1/2 (14 × 12)

= 1/2 (168)

= 84 cm²

So, the area of the rhombus = 84 cm².

Problem 9 :

The bases of a trapezoid are 24 feet and 16 feet. The height of the trapezoid is12 feet. What is the area of the trapezoid?

Solution :

Given,

Base (b₁) = 24 ft, Base (b₂) = 16 ft and Height (h) = 12 ft

Area of a trapezoid A = 1/2  (b₁ + b₂) × h

= 1/2  (24 + 16) × 12

= 1/2 (40) × 12

= 240 ft²

So, the area of the trapezoid = 240 ft²