Area and Perimeter

The area of a square is given by the formula A = s^2, where s is the length of a side. In this case, s = 5 cm, so A = 5^2 = 25 cm^2.

The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. In this case, l = 8 cm and w = 6 cm, so P = 2(8 + 6) = 2(14) = 28 cm.

The perimeter of a triangle is given by the formula P = a + b + c, where a, b, and c are the lengths of the sides. In this case, a = 3 cm, b = 4 cm, and c = 5 cm, so P = 3 + 4 + 5 = 12 cm.

The area of a circle is given by the formula A = πr^2, where r is the radius. In this case, r = 7 cm, so A = π(7)^2 = 154 cm^2.

The total length of the fence is equal to the perimeter of the garden. The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. In this case, l = 10 m and w = 8 m, so P = 2(10 + 8) = 2(18) = 36 m.

The area of a square is given by the formula A = s^2, where s is the length of a side. In this case, A = 36 cm^2, so s^2 = 36. Taking the square root of both sides, we get s = √36 = 6 cm.

The circumference of a circle is given by the formula C = 2πr, where r is the radius. In this case, C = 22 cm, so 2πr = 22. Dividing both sides by 2π, we get r = 22 / 2π ≈ 3.5 cm.

The perimeter of a triangle is given by the formula P = a + b + c, where a, b, and c are the lengths of the sides. In this case, a = 12 m, b = 15 m, and c = 18 m, so P = 12 + 15 + 18 = 45 m.

The area of a rectangle is given by the formula A = l * w, where l is the length and w is the width. In this case, l = 9 m and w = 6 m, so A = 9 * 6 = 54 m^2.

The area of a circle is given by the formula A = πr^2, where r is the radius. In this case, A = 1256 cm^2, so πr^2 = 1256. Dividing both sides by π, we get r^2 = 1256 / π ≈ 400. Taking the square root of both sides, we get r ≈ 20 cm.

The perimeter of a square is given by the formula P = 4s, where s is the length of a side. In this case, P = 40 cm, so 4s = 40. Dividing both sides by 4, we get s = 40 / 4 = 10 cm.

The total area of the fence is equal to the area of the rectangle plus the area of the four sides of the fence. The area of the rectangle is given by the formula A = l * w, where l is the length and w is the width. In this case, l = 15 m and w = 10 m, so A = 15 * 10 = 150 m^2. The area of the four sides of the fence is given by the formula A = 2(l + w) * h, where h is the height of the fence. In this case, l = 15 m, w = 10 m, and h = 2 m, so A = 2(15 + 10) * 2 = 2(25) * 2 = 100 m^2. Therefore, the total area of the fence is 150 + 100 = 250 m^2.

The area of a triangle is given by the formula A = √s(s - a)(s - b)(s - c), where s is the semiperimeter and a, b, and c are the lengths of the sides. In this case, s = (20 + 25 + 30) / 2 = 37.5 m. Therefore, A = √37.5(37.5 - 20)(37.5 - 25)(37.5 - 30) = √37.5 * 17.5 * 12.5 * 7.5 = 300 m^2.

The circumference of a circle is given by the formula C = 2πr, where r is the radius. In this case, C = 56.52 cm, so 2πr = 56.52. Dividing both sides by 2π, we get r = 56.52 / 2π ≈ 9 cm. Therefore, the area of the circle is given by the formula A = πr^2 = π(9)^2 ≈ 274.87 cm^2.

The area of the carpet is equal to the area of the floor of the room. The area of a rectangle is given by the formula A = l * w, where l is the length and w is the width. In this case, l = 12 m and w = 8 m, so A = 12 * 8 = 96 m^2.