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In this lesson, we will learn how to find the area of a square in terms of its diagonal, where the area equals half the square of the length of the diagonal.

Q1:

Find the area of a square with a diagonal of 3 cm.

Q2:

The area of the square is cm^{2}. Find the length of .

Q3:

The diagonal length of a square is 42.5 cm. Find its area. Round the result to the nearest tenth.

Q4:

Given that π· π = 4 . 5 c m , find the area of the square.

Q5:

I have a piece of paper with area 190 cm^{2}. I cut out 4 congruent squares which each have a diagonal length of 8 cm. What is the area of the paper I have left?

Q6:

I have a piece of paper with area 231 cm^{2}. I cut out 5 congruent squares which each have a diagonal length of 8 cm. What is the area of the paper I have left?

Q7:

What is the diagonal length of a square which has an area of 8 cm^{2}?

Q8:

What is the diagonal length of a square which has an area of 1 2 1 2 cm^{2}?

Q9:

Find the diagonal length of a square whose area equals that of a rectangle having dimensions of 10 cm and 35 cm.

Q10:

Find the area of a square whose diagonal is 9 cm.

Q11:

Find the area of a square whose diagonal is 6 cm.

Q12:

Find the area of a square whose diagonal is 7 cm.

Q13:

Determine the side length of a square having an area of 4 cm^{2}.

Q14:

A square has a diagonal 29. What is its area?

Q15:

Given that the area of each square on the chessboard is 81 cm^{2}, find the diagonal length of the chessboard.

Q16:

A square has an area of 147 cm^{2}. Determine the length of its side.

Q17:

Find the difference between the area of a square whose side length is 17 cm and the area of a square whose diagonal length is 20 cm.

Q18:

What is the side length of a square whose area is 448 cm^{2}?

Q19:

Find the area of a square, to the nearest hundredth, if half the length of its diagonal is 12.72 cm.

Q20:

What is the area of this square?

Q21:

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