Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Lesson: Area of a Square from the Diagonal Length

Sample Question Videos

Worksheet • 21 Questions • 2 Videos

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 𝐷 𝑂 = 4 . 5 c m , 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 62 cm2
  • B 94 cm2
  • C 128 cm2
  • D 66 cm2
  • E 158 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 71 cm2
  • B 103 cm2
  • C 160 cm2
  • D 89 cm2
  • E 199 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 1 2 1 2 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 1 0 √ 7 cm
  • B 1 0 √ 2 cm
  • C 18 cm
  • D 3 5 √ 2 cm

Q10:

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

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

Q11:

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

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

Q12:

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

  • A 4 9 2 cm2
  • B 49 cm2
  • C 14 cm2
  • D 28 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 7 2 √ 2 cm
  • B 5 184 cm
  • C 72 cm
  • D 648 cm
  • E 3 6 √ 2 cm

Q16:

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

  • A 7 √ 3 cm
  • B 73 cm
  • C 7 √ 3 2 cm
  • D 12 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 89 cm2
  • B 489 cm2
  • C 511 cm2
  • D 111 cm2

Q18:

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

  • A 8 √ 7
  • B224
  • C 4 √ 7
  • D21

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?

Preview