Question

topic 1: area of a square
question 1 find the area of the following squares.
question 2 find the area of the square whose side is given below. (show all your working.)
question 3 find the length of the side of the square whose area is given below. (show all
working.)

Explanation:

Step1: Area formula of square

The area formula of a square is \(A = s^2\), where \(s\) is the side - length of the square.

Step2: Solve Question 1a

For the square in Question 1a with \(s = 4\space cm\), using the formula \(A=s^{2}\), we have \(A = 4^{2}=16\space cm^{2}\).

Step3: Solve Question 1b

For the square in Question 1b with \(s = 5\space cm\), using the formula \(A=s^{2}\), we have \(A = 5^{2}=25\space cm^{2}\).

Step4: Solve Question 1c

For the square in Question 1c with \(s = 8\space cm\), using the formula \(A=s^{2}\), we have \(A = 8^{2}=64\space cm^{2}\).

Step5: Solve Question 1d

For the square in Question 1d with \(s = 7\space cm\), using the formula \(A=s^{2}\), we have \(A = 7^{2}=49\space cm^{2}\).

Step6: Solve Question 1e

For the square in Question 1e with \(s = 9\space cm\), using the formula \(A=s^{2}\), we have \(A = 9^{2}=81\space cm^{2}\).

Step7: Solve Question 1f

For the square in Question 1f with \(s = 6\space cm\), using the formula \(A=s^{2}\), we have \(A = 6^{2}=36\space cm^{2}\).

Step8: Solve Question 2a

For the square in Question 2a with \(s = 3\space m\), using the formula \(A=s^{2}\), we have \(A = 3^{2}=9\space m^{2}\).

Step9: Solve Question 2b

For the square in Question 2b with \(s = 10\space m\), using the formula \(A=s^{2}\), we have \(A = 10^{2}=100\space m^{2}\).

Step10: Solve Question 2c

For the square in Question 2c with \(s = 11\space cm\), using the formula \(A=s^{2}\), we have \(A = 11^{2}=121\space cm^{2}\).

Step11: Solve Question 2d

For the square in Question 2d with \(s = 1.5\space m\), using the formula \(A=s^{2}\), we have \(A=(1.5)^{2}=2.25\space m^{2}\).

Step12: Solve Question 2e

For the square in Question 2e with \(s = 12\space mm\), using the formula \(A=s^{2}\), we have \(A = 12^{2}=144\space mm^{2}\).

Step13: Solve Question 2f

For the square in Question 2f with \(s = 3.2\space m\), using the formula \(A=s^{2}\), we have \(A=(3.2)^{2}=10.24\space m^{2}\).

Step14: Side - length formula of square

Since \(A = s^{2}\), then \(s=\sqrt{A}\).

Step15: Solve Question 3a

For the square in Question 3a with \(A = 16\space cm^{2}\), using the formula \(s=\sqrt{A}\), we have \(s=\sqrt{16}=4\space cm\).

Step16: Solve Question 3b

For the square in Question 3b with \(A = 169\space m^{2}\), using the formula \(s=\sqrt{A}\), we have \(s=\sqrt{169}=13\space m\).

Step17: Solve Question 3c

For the square in Question 3c with \(A = 49\space m^{2}\), using the formula \(s=\sqrt{A}\), we have \(s=\sqrt{49}=7\space m\).

Step18: Solve Question 3d

For the square in Question 3d with \(A = 225\space cm^{2}\), using the formula \(s=\sqrt{A}\), we have \(s=\sqrt{225}=15\space cm\).

Step19: Solve Question 3e

For the square in Question 3e with \(A = 256\space cm^{2}\), using the formula \(s=\sqrt{A}\), we have \(s=\sqrt{256}=16\space cm\).

Step20: Solve Question 3f

For the square in Question 3f with \(A = 676\space mm^{2}\), using the formula \(s=\sqrt{A}\), we have \(s=\sqrt{676}=26\space mm\).

Answer:

Question 1:
a. \(16\space cm^{2}\)
b. \(25\space cm^{2}\)
c. \(64\space cm^{2}\)
d. \(49\space cm^{2}\)
e. \(81\space cm^{2}\)
f. \(36\space cm^{2}\)

Question 2:
a. \(9\space m^{2}\)
b. \(100\space m^{2}\)
c. \(121\space cm^{2}\)
d. \(2.25\space m^{2}\)
e. \(144\space mm^{2}\)
f. \(10.24\space m^{2}\)

Question 3:
a. \(4\space cm\)
b. \(13\space m\)
c. \(7\space m\)
d. \(15\space cm\)
e. \(16\space cm\)
f. \(26\space mm\)