Aright triangular prism is constructed so that it’s height is equal to the leg length of the base. what expression represents the volume of the prism, in cubic units? a. 1/2x^3 b. 1/2x^2+x c. 2x^3 d. 2x^2+x

Option A is correct.

The volume of prism= cubic units

Explanation:

Volume of the right triangular prism(V) is given by the formula:

; where B is the area of the  base, and h is the height.

Given: The height of the prism(h) = x unit

The base (B) in the given figure of the prism is the right triangle with legs of length x unit and base x unit.

Area of the right angle triangle is given by: (A) = where b is the base and l is the height of the triangle respectively.

Therefore,

B = = square unit

Substitute the value of base and height in the above given formula of volume of prism,

therefore,

Volume of the prism (V) = Bh cubic unit

                                        =

                                        = cubic units

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given   that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency   kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule   states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.

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