The Formula for the Area of a Parallelogram,
Area = b × h sq. units.
(where b is the base and h is the height)
The Formula for the Area of a trapezoid,
Area = 1/2 (b_{1} + b_{2}) × h sq. units.
(where b_{1} and b_{2 }are the bases, h is the height)
The Formula for the Area of a Rhombus,
Area = 1/2 (d_{1} × d_{2}) sq. units.
(where d_{1} and d_{2 }are the diagonals)
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 ft^{2}
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 m^{2}
Find the area of each trapezoid .
Problem 3 :
Solution :
By observing the figure,
Base (b_{1}) = 12 in, Base (b_{2}) = 5 in and Height (h) = 4 in.
Area of a trapezoid A = 1/2 (b_{1} + b_{2}) × h
= 1/2 (12 in + 5 in) × 4 in
= 1/2 (17 in) × 4 in
Area = 34 in^{2}
Problem 4 :
Solution :
By observing the figure,
Base (b_{1}) = 6 ft, Base (b_{2}) = 2 ft, and Height (h) = 2 ft
Area of a trapezoid A = 1/2 (b_{1} + b_{2}) × h
= 1/2 (6 + 2) × 2
= 1/2 (8) × 2
Area = 8 ft^{2}
Find the area of each rhombus.
Problem 5 :
Solution :
By observing the figure,
Diagonal (d_{1}) = 6 cm and Diagonal (d_{2}) = 9 cm
Area of a rhombus A = 1/2 (d_{1} × d_{2})
= 1/2 (6 × 9)
= 1/2 (54)
= 27 cm^{2}
Problem 6 :
Solution :
By observing the figure,
Diagonal (d_{1}) = 12 in. and Diagonal (d_{2}) = 18 in.
Area of a rhombus A = 1/2 (d_{1} × d_{2})
= 1/2 (12 in × 18 in)
= 1/2 (216 in^{2})
Area = 108 in^{2}
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 in^{2}
So, the area of the desktop = 1200 in^{2}
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 (d_{1}) = 14 cm and Diagonal (d_{2}) = 12 cm
Area of a rhombus A = 1/2 (d_{1} × d_{2})
= 1/2 (14 × 12)
= 1/2 (168)
= 84 cm^{2}
So, the area of the rhombus = 84 cm^{2}.
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 (b_{1}) = 24 ft, Base (b_{2}) = 16 ft and Height (h) = 12 ft
Area of a trapezoid A = 1/2 (b_{1} + b_{2}) × h
= 1/2 (24 + 16) × 12
= 1/2 (40) × 12
= 240 ft^{2}
So, the area of the trapezoid = 240 ft^{2}
May 21, 24 08:51 PM
May 21, 24 08:51 AM
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