The area formula is used to find the number of square units a polygon encloses. The figure below shows some area formulas that are frequently used in the classroom or in the real-world.
The area of a square is the square of the length of one side. Let s be the length of one side.
A = s^{2} = s × s
The area of a rectangle is the product of its base and height.
Let b = base and let h = height
A = b × h = bh
For a rectangle, "length" and "width" can also be used instead of "base" and "height"
The area of a rectangle can also be the product of its length and width
A = length × width
The area of a circle is the product of pi and the square of the radius of the circle.
Let r be the radius of the circle and let pi = π = 3.14
A = πr^{2}
Please see the lesson about area of a circle to get a deeper knowledge.
The area of a triangle is half the product of the base of the triangle and its height.
Let b = base and let h = height
Area = (b × h)/2
The area of a parallelogram is the product of its base and height.
Let b = base and let h = height
A = b × h = bh
Please see the lesson about parallelogram to learn more.
The area of a rhombus / area of a kite is half the product of the lengths of its diagonals.
Let d_{1} be the length of the first diagonal and d_{2} the length of the second diagonal.
A = (d_{1} × d_{2})/2
The area of a trapezoid is half the product of the height and the sum of the bases.
Let b_{1} be the length of the first base, b_{2} the length of the second base, and let h be the height of the trapezoid.
A = [h(b_{1} + b_{2})]/2
Please see the lesson about area of a trapezoid to learn more.
The area of the ellipse is the product of π, the length of the semi-major axis, and the length of the semi-minor axis.
Let a be the length of the semi-major axis and b the length of the semi-minor axis.
A = πab
The semi-major axis is also called major radius and the semi-minor axis is called minor radius.
Let r_{1} be the length of the semi-major axis and r_{2} the length of the semi-minor axis.
The area is also equal to πr_{1}r_{2}
Example #1
What is the area of a rectangular backyard whose length and breadth are 50 feet and 40 feet respectively?
Solution:
Length of the backyard = 50 ft
Breadth of the backyard = 40 ft
Area of the backyard = length × breadth
Area of the backyard = 50 ft × 40 ft
Area of the backyard = 2000 square feet = 2000 ft^{2}
Example #2
The lengths of the adjacent sides of a parallelogram are 12 cm and 15 cm. The height corresponding to the 12-cm base is 6 cm. Find the height corresponding to the 15-cm base.
Solution:
A = b × h = 12 × 6 = 72 cm^{2}
Since the area is still the same, we can use it to find the height corresponding to the 15 cm base.
A = b × h
Substitute 72 for A and 15 for b.
72 = 15 × h
Divide both sides of the equation by 15
72/15 = (15/15) × h
4.8 = h
The height corresponding to the 15 cm base is 4.8 cm.
Example #3
The diameter of a circle is 9. What is the area of the circle?
Solution:
Since the radius is half the diameter, r = 9/2 = 4.5
A = πr^{2}
A = 3.14(4.5)^{2}
A = 3.14(20.25)
A = 63.585
Jan 26, 23 11:44 AM
Jan 25, 23 05:54 AM