Question

lesson = volume of a prism question 3 of 10
the figure shown is a trapezoidal/trapezium prism which has the cross section of a trapezium/trapezoid with the following dimensions:
a = 15 cm
b = 17 cm
h = 16 cm (height of the trapezium/trapezoid)
h = 30 cm (height of the prism)
what is the volume of this prism?

Explanation:

Step1: Calculate the area of the trapezoidal cross - section

The formula for the area of a trapezoid is \(A=\frac{(a + b)h}{2}\).
Substitute \(a = 15\space cm\), \(b = 17\space cm\) and \(h = 16\space cm\) into the formula:

$$
LATEXBLOCK0
$$

Step2: Calculate the volume of the prism

The formula for the volume of a prism is \(V=A\times H\), where \(A\) is the area of the cross - section and \(H\) is the height of the prism.
Substitute \(A = 256\space cm^{2}\) and \(H = 30\space cm\) into the formula:
\(V=256\times30 = 7680\space cm^{3}\)

Answer:

\(7680\space cm^{3}\)