Sample Problems
Problem 1: What is the total area (in square feet) of the hall, if the hall is in the shape of a square with each of its sides measuring 13 ft?
Solution:
Given,
Length of each side of the square hall = 13 ft
We have,
Square footage formula of a square = (side)2
= (13)2 = 169
Hence, the area of the square hall is 169 sq. ft.
Problem 2: What is the total area (in square feet) of the circular field if its radius is 15 ft? [π = 3.14]
Solution:
Given,
Radius of the circular field (r) = 15 ft
We have,
Square footage formula of a circle = πr2
= 3.14 × (15)2
= 3.14 × 225 = 706.5
Hence, the area of the circular field is 706.5 sq. ft.
Problem 3: Calculate the base length of a triangular surface whose total area and height are 240 sq. ft. and 20 ft., respectively.
Solution:
Given,
Total area of the triangular surface = 240 sq. ft
Height of the triangular surface = 20 ft.
We have,
Area of the triangular surface = ½ × base × height
⇒ 240 = 1/2 × b × 20
⇒ 10b = 240
⇒ b = 240/10 = 24 ft
Hence, the base length of the triangular surface is 24 ft.
Problem 4: Calculate the area or surface footage of a parallelogram whose base and height are 7 ft and 9 ft, respectively.
Solution:
Given,
Base of a parallelogram = 7 ft
Height of the parallelogram = 9 ft
We have,
Square footage formula for a parallelogram = base × height
= 7 × 9 = 63 sq. ft
Problem 5: Determine the length of the rectangular field if its area and breadth are 1800 sq. ft. and 40 ft.
Solution:
Given,
Square footage of the rectangular surface = 1800 sq. ft
Breadth = 40 ft
The square footage formula for rectangular surface = length × breadth
⇒ 1800 = l × 40
⇒ l = 1800/40 = 45 ft
Hence, the length of the rectangular field is 45 ft.
Problem 6: Determine the height of the trapezoid if its square footage is 480 sq. ft. and the lengths of its parallel sides are 12 ft and 18 ft, respectively.
Solution:
Given,
Square footage of a trapezoid = 480 sq. ft.
Lengths of its parallel sides are 12 ft and 18 ft
a = 12 ft and b = 18 ft
We know that,
Square Footage of a Trapezoid = [½ × h (a + b)] sq. ft.
⇒ 480 = 1/2 × h (12 + 18)
⇒ 480 = 1/2 × h × 30
⇒ 15h = 480
⇒ h = 480/15 = 32 ft
Hence, the height of the given trapezoid is 32 ft.
How to calculate Square Footage?
Square foot, or square footage, is an imperial unit of area measurement. The area of a two-dimensional shape is defined as the amount of space enclosed within the perimeter of the shape. The area of a square, rectangle, circle, etc. is measured in square units. The area of a two-dimensional object differs from one shape to the other, where we have different 2D objects of various shapes, such as squares, circles, kites, rectangles, parallelograms, etc. The area of an object is expressed quantitatively using SI-derived units like a square meter or by using various imperial units like square feet, square yards, acres, hectares, etc.
In this article, we will learn about the definition of a square foot and its conversion to other units.