Question

Find the volume of the given shape​

Answer 1

`{ \tt{volume = base \: area * height * length}} \\ \\ { \tt{v = (1)/(2) (a + b) * h * l }} \\ \\ { \tt{v = (1)/(2) (1.7 + 2.3) * 1.3 * 1.5}} \\ \\ { \tt{v = 2 * 1.3 * 1.5}} \\ \\{ \tt{v = 3.9 \: {m}^(3) }}`

Answer 2

3.9 m³

Explanation:

To find the volume of a right prism, multiply its base area by its height.

For the given shape:

• Base = trapezoid ABCD
• Height = 1.5 m

Area of a trapezoid

`\boxed{A = (1)/(2)(a+b)h}`

Where a and b are the bases and h is the height.

From inspection of the given diagram:

• a = BC = 1.7 m
• b = AD = 2.3 m
• h = CD = 1.3 m

Substitute the given values into the formula to find the area of the trapezoid base (ABCD):

`\begin{aligned}A & = (1)/(2)(a+b)h\\\implies ABCD & = (1)/(2)(BC+AD)CD\\ &=(1)/(2)(1.7+2.3)(1.3)\\&=(1)/(2)(4)(1.3)\\&=(2)(1.3)\\&=2.6\; \sf m^2\end{aligned}`

Therefore:

`\begin{aligned}\textsf{Volume of prism} & = \textsf{Area of base} * \sf height\\\implies V & = ABCD * 1.5\\V & = 2.6 * 1.5\\V & = 3.9\;\sf m^3\end{aligned}`