# 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.

**Q4: **

What is the area of this square?

**Q5: **

Given that , find the area of the square.

**Q6: **

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

**Q7: **

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?

**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.

**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 cm
- C cm
- D cm

**Q13: **

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

- A72 cm
- B cm
- C5,184 cm
- D648 cm
- E cm

**Q14: **

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?

**Q15: **

What is the diagonal length of a square which has an area of 50 cm^{2}?

**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.

**Q21: **

From an 18 by 23 rectangular sheet of paper are cut out six squares, each of diagonal 7. What is the area of the remaining part?