**Calculating Areas and Perimeters of Squares**

**Area of a square: A = s^2, where s is the length of one of its sides**

**Perimeter of a square: P = 4s, where s is the length of one of its sides**

**Question 1:**

**A square has a perimeter of 28cm. What is its area?**

**Solution:**

**P = 4s**

**28 = 4s**

**s = 7cm**

**__A = s^2**

**A = 7^2**

**A = 49cm^2**

**Requested by: Anonymous**

**Question 2:**

**Find the perimeter of a square with a side length of 5cm.**

**Solution:**

**P = 4s**

**P = 4(5)**

**P = 20cm**

**Requested by: Anonymous**

**Question 3:**

**Find the area of a square with a side length of 8cm.**

**Solution:**

**A = s^2**

**A = 8^2**

**A = 64cm^2**

**Requested by: Arslan**

**Question 4: **

**Find the area and perimeter of a square with a side length of 6 cm.**

**Solution:**

**Area = s^2 = 6 cm * 6 cm = 36 cm^2**

**Perimeter = 4s = 4 * 6 cm = 24 cm**

**Requested by: Ritaaj**

**Question 5:**

**Find the area of a square with perimeter 32 cm.**

**Solution:**

**Perimeter = 4s, where s is the side length of the square.**

**32 cm = 4s**

**s = 8 cm**

**Therefore, the area of the square is:**

**Area = s^2 = 8 cm * 8 cm = 64 cm^2**

**Requested by: Ritaaj**

**Question 6: **

**Find the area and perimeter of a square with a diagonal length of 10 cm.**

**Solution:**

**To find the side length of the square, we can use the Pythagorean theorem:**

**a^2 + b^2 = c^2, where a and b are the length of the two sides and c is the length of the hypotenuse (the diagonal of the square).**

**In a square, a = b, so we have:**

**2a^2 = c^2**

**a^2 = (1/2)c^2**

**a = (1/2)c (since a must be positive and smaller than c)**

**Therefore, the side length of the square is:**

**s = a = (1/2)c = (1/2) * 10 cm = 5 cm**

**Area = s^2 = 5 cm * 5 cm = 25 cm^2**

**Perimeter = 4s = 4 * 5 cm = 20 cm**

**Requested by: Ritaaj**

**Question 7:**

**A square has a perimeter of 28cm. What is the length of each side?**

**Solution:**

**Perimeter of a square = 4s, **

**where s is the length of each side.**

**Given, perimeter = 28cm**

**28 = 4s**

**s = 7cm**

**Requested by: Mustakeem**

**Question 8:**

**A square has a diagonal of 6√2 cm. What is the area of the square?**

**Solution:**

**Area of a square = s^2, where s is the length of each side.**

**The diagonal of a square is the hypotenuse of a right-angled triangle with sides s and s.**

**Given, diagonal = 6√2 cm**

**By Pythagoras theorem, (s^2 + s^2) = (6√2)^2**

**2s^2 = 72**

**s^2 = 36**

**Area = s^2 = 36cm^2**

**Requested by: Mustakeem**

**Question 9:**

**A square has an area of 121m^2. What is the length of each side?**

**Solution:**

**Area of a square = s^2, where s is the length of each side.**

**Given, area = 121m^2**

**s^2 = 121**

**s = 11m**

**Requested by: Faisal**

**Question 10:**

**A square has a perimeter of 40mm. What is the area of the square?**

**Solution:**

**Perimeter of a square = 4s, where s is the length of each side.**

**Given, perimeter = 40mm**

**40 = 4s**

**s = 10mm**

**Area = s^2 = 100mm^2**

**Requested by: Faisal**

**Question 11:**

**Find the perimeter of a square with side length 6cm.**

**Solution:**

**P = 4s**

**P = 4(6)**

**P = 24cm**

**Requested by: Anonymous**

**Question 12:**

**Find the area of a square with side length 8cm.**

**Solution:**

**A = s^2**

**A = 8^2**

**A = 64cm^2**

**Requested by: Khalid**

**Question 13:**

**A square has a perimeter of 36m. What is the length of each side?**

**Solution:**

**P = 4s**

**36 = 4s**

**s = 9m**

**Requested by: Khalid**

**Question 14:**

**A square has an area of 49cm^2. What is the length of each side?**

**Solution:**

**A = s^2**

**49 = s^2**

**s = 7cm**

**Requested by: Khalid**

**Question 15:**

**Find the perimeter of a square with diagonal length 10cm.**

**Solution:**

**Let s be the side length of the square.**

**By Pythagoras theorem: s^2 + s^2 = 10^2**

**2s^2 = 100**

**s^2 = 50**

**s = √50 cm**

**P = 4s**

**P = 4(√50)**

**P = 4(5√2) cm**

**Requested by: Khalid**

**Question 16:**

**A square has an area of 169cm^2. Find the length of its side.**

**Solution:**

**A = s^2**

**169 = s^2**

**s = √169**

**s = 13cm**

**Requested by: Mansoor**

**Question 17:**

**A square has a perimeter of 64cm. Find the length of its side.**

**Solution:**

**P = 4s**

**64 = 4s**

**s = 16cm**

**Requested by: Mansoor**

**Question 18:**

**Find the perimeter of a square with an area of 49cm^2.**

**Solution:**

**A = s^2**

**49 = s^2**

**s = 7cm**

**P = 4s**

**P = 4(7)**

**P = 28cm**

**Requested by: Mansoor**

**Question 19:**

**A square has a perimeter of 40cm. Find its area.**

**Solution:**

**P = 4s**

**40 = 4s**

**s = 10cm**

**A = s^2**

**A = 10^2**

**A = 100cm^2**

**Requested by: Mansoor**

**Question 20:**

**Find the perimeter of a square with a diagonal of 10cm.**

**Solution:**

**P = 4s**

**d = √2s**

**10 = √2s**

**s = 10/√2**

**P = 4(10/√2)**

**P ≈ 28.28cm**

**Requested by: Haroon**

**Question 21:**

**Find the area of a square with a diagonal of 12cm.**

**Solution:**

**d = √2s**

**12 = √2s**

**s = 12/√2**

**A = s^2**

**A = (12/√2)^2**

**A ≈ 144cm^2**

**Requested by: Haroon**

**Question 22:**

**Find the perimeter of a square with an area of 81cm^2.**

**Solution:**

**A = s^2**

**81 = s^2**

**s = 9cm**

**P = 4s**

**P = 4(9)**

**P = 36cm**

**Requested by: Haroon**

**Question 23:**

**A square has a diagonal of 10cm. Find its area.**

**Solution:**

**d = √2s**

**10 = √2s**

**s = 10/√2**

**A = s^2**

**A = (10/√2)^2**

**A ≈ 50cm^2**

**Requested by: Haroon**

**Question 24:**

**Find the perimeter of a square with a side length of 3.5cm.**

**Solution:**

**P = 4s**

**P = 4(3.5)**

**P = 14cm**

**Requested by: Bilal**

**Question 25:**

**Find the area of a square with a perimeter of 20cm.**

**Solution:**

**P = 4s**

**20 = 4s**

**s = 5cm**

**A = s^2**

**A = 5^2**

**A = 25cm^2**

**Requested by: Bilal**

**Question 26:**

**A square has an area of 25cm^2. Find its perimeter.**

**Solution:**

**A = s^2**

**25 = s^2**

**s = 5cm**

**P = 4s**

**P = 4(5)**

**P = 20cm**

**Requested by: Bilal**

**Question 27:**

**A square has a diagonal of 8cm. Find its perimeter.**

**Solution:**

**d = √2s**

**8 = √2s**

**s = 8/√2**

**P = 4s**

**P = 4(8/√2)**

**P ≈ 22.63cm**

**Requested by: Bilal**

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