Answer
Verified
399.3k+ views
Hint: Use the property that area of the square is equal to half of the square of the length of the diagonal of the square, i.e., area of the square is $\dfrac{{{l}^{2}}}{2}$ , where l is the length of the diagonal. So, just put the length of the diagonal in the formula and solve to get the answer.
Complete step-by-step answer:
Let us start the solution to the above question by drawing a representative diagram of the situation given in the figure.
Now we know that the area of the square is equal to half of the square of the length of the diagonal of the square.
$\therefore \text{ Area of the square = }\dfrac{{{\left( diagonal \right)}^{2}}}{2}$
Now, it is given that the length of the diagonal of the square is 8cm. So, if we put this in our equation, we get
$\text{Area of the square = }\dfrac{{{8}^{2}}}{2}$
Now, we know that the square of 8 is equal to 64.
$\text{Area of the square = }\dfrac{64}{2}=32c{{m}^{2}}$
Therefore, the area of the square whose diagonal is 8 cm in length is equal to 32 sq cm.
Hence, the answer to the above question is option (d).
Note: We could have also solved the above question using the property that the diagonal of a square is $\sqrt{2}$ times the length of its side followed by the use of the formula that the area of the square is equal to the square of the length of its side.
Complete step-by-step answer:
Let us start the solution to the above question by drawing a representative diagram of the situation given in the figure.
Now we know that the area of the square is equal to half of the square of the length of the diagonal of the square.
$\therefore \text{ Area of the square = }\dfrac{{{\left( diagonal \right)}^{2}}}{2}$
Now, it is given that the length of the diagonal of the square is 8cm. So, if we put this in our equation, we get
$\text{Area of the square = }\dfrac{{{8}^{2}}}{2}$
Now, we know that the square of 8 is equal to 64.
$\text{Area of the square = }\dfrac{64}{2}=32c{{m}^{2}}$
Therefore, the area of the square whose diagonal is 8 cm in length is equal to 32 sq cm.
Hence, the answer to the above question is option (d).
Note: We could have also solved the above question using the property that the diagonal of a square is $\sqrt{2}$ times the length of its side followed by the use of the formula that the area of the square is equal to the square of the length of its side.
Recently Updated Pages
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Find the values of other five trigonometric functions class 10 maths CBSE
Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
What organs are located on the left side of your body class 11 biology CBSE
Write an application to the principal requesting five class 10 english CBSE
What is the type of food and mode of feeding of the class 11 biology CBSE
Name 10 Living and Non living things class 9 biology CBSE