Answer:
Below
Step-by-step explanation:
Let D be the diagonal of this square.
D forms with AB and BC a right triangle where D is the hypotenus.
We will apply then the Pythagorian theorem
●The Pythagorian theorem
● D^2 = AB^2 + BC^2
ABCD is a square, so AB=BC
● D^2 = AB^2 + AB^2
● D^2 = 2AB^2
We khow that is D= 5 cm
● 25 = 2AB^2
● 25/2 = AB^2
● 5/√2 = AB
AB is 5√2 cm
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The perimeter is:
● P = 4AB
● P = 4×(5/√2)
● P = 20/√2
● P = 10×2/√2
● P = 10√2 cm
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The area is
● A = AB^2
● A = (5/√2)^2
● A = 25/2 cm^2
Answer:
Step-by-step explanation:
the sides of a square are equal ( AB=BC=CD=DA)
diagonal of the square creates two right angle triangle
to find the side of the triangle we apply the Pythagorean theorem:
a²+b²=c² ( let AB=a, and BC=b)
2a²=25 ( since AB=BC=a)
a²=25/2
a=(5√2)/2 cm
a=3.54 ( rounded to the nearest 10)
perimeter = 4a
P=4(5√2/2)
P=10√2 cm
Area=a²=(5√2/2)²=25/2=12.5 cm^2
