# Worksheet: Area of a Square from the Diagonal Length

Q1:

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

Q2:

The area of the square is cm2. 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 , find the area of the square.

Q5:

I have a piece of paper with area 190 cm2. 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?

• A 158 cm2
• B 128 cm2
• C 66 cm2
• D 62 cm2
• E 94 cm2

Q6:

I have a piece of paper with area 231 cm2. 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?

• A 199 cm2
• B 160 cm2
• C 89 cm2
• D 71 cm2
• E 103 cm2

Q7:

What is the diagonal length of a square which has an area of 8 cm2?

Q8:

What is the diagonal length of a square which has an area of cm2?

Q9:

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

• A cm
• B cm
• C 18 cm
• D cm

Q10:

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

• A 36 cm2
• B 81 cm2
• C 18 cm2
• D cm2

Q11:

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

• A 24 cm2
• B 36 cm2
• C 12 cm2
• D 18 cm2

Q12:

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

• A 28 cm2
• B 49 cm2
• C 14 cm2
• D cm2

Q13:

Determine the side length of a square having an area of 4 cm2.

Q14:

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

Q15:

Given that the area of each square on the chessboard is 81 cm2, find the diagonal length of the chessboard.

• A cm
• B 72 cm
• C 648 cm
• D cm
• E 5β184 cm

Q16:

A square has an area of 147 cm2. Determine the length of its side.

• A 12 cm
• B 73 cm
• C cm
• D cm

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.

• A 111 cm2
• B 489 cm2
• C 511 cm2
• D 89 cm2

Q18:

What is the side length of a square whose area is 448 cm2?

• A21
• B224
• C
• D

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:

What is the area of this square?