David has a triangular prism that has an equilateral base. Also, the base of the prism is of the same length as its height. Pick all the possible shapes that can be obtained either by horizontal or vertical slicing through the prism

a) Triangle

b) Rectangle

Step-by-step explanation:

A triangular prism that has an equilateral base and a height with the same length as the base of the prism.

a) Shape from horizontal slicing

A plane parallel to the base of a triangular prism will  intersect a cross section that is the same shape as its  bases. So the cross section of the horizontal slicing is an equilateral triangle (all the sides of the triangle are equal).

b) Shape from vertical slicing

If the triangular prism is sliced vertically, the resulting shape would be a rectangle with a length that is the same as the base of the prism.

395.84

step-by-step explanation:

2πrh+2πr²

2 (pie)(radius)(height)+2(pie)(radius)^2

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.