The perimeter of a square is 81 cm. Find its area.
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What is the area if the perimeter of a square is 81 cm?
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5 Answers
William Mccoy
William Mccoy, A former high school math teacher (Grades 9, 10, and 11). I have a Bachelor of Science Degree in Math Ed. (...
Answered Mar 5, 2018 · Author has 2.6k answers and 8.1m answer views
The formula for the area of a square is: A = s², where s is the length of one of the 4 congruent sides of the square.
The formula for the perimeter (the distance around) a square is given by:
P = 4s.
Since we're given that P = 81 cm, we can substitute this information into the formula for the perimeter P in order to find s, and thus finally determine area A of the square as follows:
P = 4s
81 cm = 4s
(81 cm)/4 = (4s)/4
20.25 cm = (4/4)s
20.25 cm = (1)s
20.25 cm = s
Now, substituting this information, i.e., s = 20.25 cm, into the formula for the area of a square, we get:
A = s²
= (20.25 cm)²
= (20.25 cm)(20.25 cm)
= 410. 1 cm² is the area of the given square rounded to then nearest tenth of a square centimeter.
Step-by-step explanation:
PERIMETER OF SQUARE =81CM
SIDE OF THE SQUARE =81÷4=20.25cm
AREA OF THE SQUARE =(20.25)*2
=410.0625sq.cm
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