# 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.

**Q3: **

The area of the square is cm^{2}. Find the length of .

**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?

- A
158 cm
^{2} - B
128 cm
^{2} - C
66 cm
^{2} - D
62 cm
^{2} - E
94 cm
^{2}

**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 cm^{2}.

**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 cm
^{2} - B
489 cm
^{2} - C
511 cm
^{2} - D
89 cm
^{2}

**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 cm
- B cm
- C 18 cm
- D cm

**Q14: **

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

- A cm
- B 72 cm
- C 648 cm
- D cm
- E 5 184 cm

**Q15: **

A square has an area of 147 cm^{2}. Determine the length of its side.

- A 12 cm
- B 73 cm
- C cm
- D cm

**Q16: **

What is the side length of a square whose area is 448 cm^{2}?

- A21
- B224
- C
- D

**Q17: **

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?

- A
199 cm
^{2} - B
160 cm
^{2} - C
89 cm
^{2} - D
71 cm
^{2} - E
103 cm
^{2}

**Q18: **

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

**Q21: **

What is the area of this square?