Question

section 5: perimeter, area & volume

1. find the area of a trapezoid with bases 8 cm and 12 cm and height 5 cm.
2. find the perimeter of a rectangle with sides 9 cm and 4 cm.
3. find the volume of a cube with side 3 cm.
4. find the surface area of a cube with side 6 cm.
5. find the volume of a rectangular prism with length 5 cm, width 3 cm, and height 4 cm.

Explanation:

Step1: Area of trapezoid formula

The formula for the area of a trapezoid is \(A=\frac{(a + b)h}{2}\), where \(a\) and \(b\) are the lengths of the bases and \(h\) is the height. Given \(a = 8\space cm\), \(b=12\space cm\), and \(h = 5\space cm\).

Step2: Substitute values into formula

Substitute the values into the formula: \(A=\frac{(8 + 12)\times5}{2}\). First, calculate the sum of the bases: \(8+12 = 20\). Then multiply by the height: \(20\times5=100\). Finally, divide by 2: \(\frac{100}{2}=50\space cm^{2}\).

Step3: Perimeter of rectangle formula

The formula for the perimeter of a rectangle is \(P = 2(l + w)\), where \(l\) is the length and \(w\) is the width. Given \(l = 9\space cm\) and \(w = 4\space cm\).

Step4: Substitute values into formula

Substitute the values into the formula: \(P=2(9 + 4)\). First, calculate the sum of length and width: \(9 + 4=13\). Then multiply by 2: \(2\times13 = 26\space cm\).

Step5: Volume of cube formula

The formula for the volume of a cube is \(V=s^{3}\), where \(s\) is the side length. Given \(s = 3\space cm\).

Step6: Substitute value into formula

Substitute the value into the formula: \(V=3^{3}=3\times3\times3 = 27\space cm^{3}\).

Step7: Surface area of cube formula

The formula for the surface area of a cube is \(SA = 6s^{2}\), where \(s\) is the side length. Given \(s = 6\space cm\).

Step8: Substitute value into formula

Substitute the value into the formula: \(SA=6\times6^{2}\). First, calculate \(6^{2}=36\). Then multiply by 6: \(6\times36=216\space cm^{2}\).

Step9: Volume of rectangular prism formula

The formula for the volume of a rectangular prism is \(V=l\times w\times h\), where \(l\) is the length, \(w\) is the width, and \(h\) is the height. Given \(l = 5\space cm\), \(w = 3\space cm\), and \(h = 4\space cm\).

Step10: Substitute values into formula

Substitute the values into the formula: \(V=5\times3\times4\). First, \(5\times3 = 15\). Then \(15\times4=60\space cm^{3}\).

Answer:

1. \(50\space cm^{2}\)
2. \(26\space cm\)
3. \(27\space cm^{3}\)
4. \(216\space cm^{2}\)
5. \(60\space cm^{3}\)