Worksheet: Area of a Square from the Diagonal Length

In this worksheet, we will practice finding 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:

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

  • A 36 cm2
  • B 81 cm2
  • C 18 cm2
  • D 8 1 2 cm2

Q3:

The area of the square is cm2. Find the length of .

Q4:

What is the area of this square?

Q5:

Given that 𝐷 𝑂 = 4 . 5 c m , find the area of the square.

Q6:

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

Q7:

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

Q8:

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

Q9:

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

Q10:

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

Q11:

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

Q12:

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

Q13:

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

  • A 3 5 2 cm
  • B 1 0 2 cm
  • C 18 cm
  • D 1 0 7 cm

Q14:

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

  • A 3 6 2 cm
  • B 72 cm
  • C 648 cm
  • D 7 2 2 cm
  • E 5 184 cm

Q15:

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

  • A 12 cm
  • B 73 cm
  • C 7 3 2 cm
  • D 7 3 cm

Q16:

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

  • A21
  • B224
  • C 4 7
  • D 8 7

Q17:

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

Q18:

What is the diagonal length of a square which has an area of 1 2 1 2 cm2?

Q19:

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

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

Q20:

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

  • A 28 cm2
  • B 49 cm2
  • C 14 cm2
  • D 4 9 2 cm2

Q21:

What is the area of this square?

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