Worksheet: Finding the Area of a Square Using Diagonals

In this worksheet, we will practice finding the area of a square in terms of its diagonal length.

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.

  • A18 cm2
  • B 8 1 2 cm2
  • C36 cm2
  • D81 cm2

Q3:

The area of the square 𝐴𝐡𝐢𝐷 is 92 cm2. Find the length of 𝐡𝐷.

Q4:

What is the area of this square?

Q5:

Given that 𝐷𝑂=4.5cm, 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?

  • A128 cm2
  • B62 cm2
  • C158 cm2
  • D66 cm2
  • E94 cm2

Q8:

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

Q9:

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

Q10:

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.

  • A111 cm2
  • B511 cm2
  • C89 cm2
  • D489 cm2

Q11:

Find the area of a square, to the nearest hundredth, if half the length of its diagonal is 3.62 cm.

Q12:

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

  • A18 cm
  • B 3 5 √ 2 cm
  • C 1 0 √ 2 cm
  • D 1 0 √ 7 cm

Q13:

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

  • A72 cm
  • B 3 6 √ 2 cm
  • C 5,184 cm
  • D648 cm
  • E 7 2 √ 2 cm

Q14:

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?

  • A160 cm2
  • B71 cm2
  • C199 cm2
  • D89 cm2
  • E103 cm2

Q15:

What is the diagonal length of a square which has an area of 50 cm2?

Q16:

Find the area of a square whose diagonal is 1 cm.

  • A2 cm2
  • B 1 2 cm2
  • C4 cm2
  • D1 cm2

Q17:

Find the area of a square whose diagonal is 11 cm.

  • A22 cm2
  • B 1 2 1 2 cm2
  • C44 cm2
  • D121 cm2

Q18:

What is the area of this square?

Q19:

What is the diagonal of a square of area 942? Round your answer to the nearest hundredth.

Q20:

Find the difference between the area of a square whose diagonal length is 6 dm and that of a parallelogram whose base length is 6 cm and height is 7 cm.

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