Question

WHAT IS THE AREA OF THE BASE AND THE VOLUME??

Answer 1

Area of the base = 6 cm²

Volume = 48 cm³

Explanation:

The given diagram shows a right triangular prism, with two triangular bases connected by three rectangular faces.

The area of the base of a right triangular prism is the area of the triangle.

The area of a triangle is half the product of its base and height.

From inspection of the given diagram, the base of the triangle is 3 cm and the height of the triangle is 4 cm. Therefore:

`\begin{aligned}\sf Area\;of\;the\;triangular\;base&=(1)/(2)\sf \cdot base \cdot height\\\\&=(1)/(2) \cdot 3 \cdot 4\\\\&=(3)/(2) \cdot 4\\\\&=(12)/(2)\\\\&=6\; \sf cm^2\end{aligned}`

Therefore, the area of the base of the prism is 6 cm².

The volume of a right prism is the product of the area of its base and its height. The height is the perpendicular distance between the two bases. So in this case, the height of the prism is 8 cm. Therefore, the volume of the prism is:

`\begin{aligned}\textsf{Volume}&=\textsf{base area} \cdot \sf height\\\\&=6 \cdot 8\\\\&=486\; \sf cm^3\end{aligned}`

Therefore, the volume of the prism is 48 cm³.