What is the volume of a hexagonal-based prism with a height of 12 in. and a base area of 62 in² ? Would the volume be different if the base were a pentagon with an area of 62 in² ? Explain.

Solution:

Given that,

Hexagonal-based prism with a height of 12 in. and a base area of 62 square inches

The volume of prism is given as:

Thus volume of a hexagonal-based prism is 744 cubic inches

Would the volume be different if the base were a pentagon with an area of 62 in² ?

No the volume will not be different

The shape of base does not matter, as long as the base area is same

Thus, volume of hexagonal-based prism and pentagon prism with area 62 inches is 744 cubic inches

$8

step-by-step explanation:

it is pretty much backwards.

you take the 4x2 multiply that, and that is = $8

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.