Question

The figure below is an oblique triangular prism.

An oblique triangular prism is shown. Triangles A B C and F E D are the triangular bases. A bisector is drawn from point E to a point on side F D. LIne F D is extended to form a right angle with a line drawn from point C with length 2. The length of F D is x squared + 3 and the height of the bisector is x. The length of A F is 2 x.

The expression below represents the volume of the figure written in standard form. What are the missing values?

axb + cx

a =

b =

c =

Answer 1

A= 1

B= 3

C=3

Explanation:

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Answer 2

Based on the calculations of this triangular prism, the missing values are a = 1, b = 3 and c = 3 respectively.

How to calculate the volume of a triangular prism?

Mathematically, the volume of a triangular prism is given by this formula:

Volume = base area × height of the prism.

Given the following data:

• Length of FD (base area) = x² + 3.

• Height of the bisector (prism) = x.

Substituting the given parameters into the formula, we have;

Volume = (x² + 3) × x

Volume = x³ + 3x

In standard form, we have:

`ax^b + cx` = x³ + 3x

Therefore, the missing values are;

a = 1.

b = 3.

c = 3.

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