The altitude of the regular quadrilateral prism is h=13 cm and lateral area is AL = 624 cm2. Find: 1) The Surface Area of the prism; 2) The Volume of the prism.

Answer:

The surface area is equal to 912 cm.

The volume is equal to 1872 cm.

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The prism is regular, which means that its bases are squares, of side v. Now you know that:

height=13
4 slant height = 624
So, side v = 12

You can now figure out that
SA (Surface area) = 912cm
Volume = 1872 cm

actually L = 6 because 6 x 13 x 24 = 1872cm cubed which his the volume i also go the answer right on my hw

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To find the surface area of the prism, we need to consider the lateral area and the area of the bases.

1) Surface Area of the prism:
Since the prism is regular, it means that the bases are regular quadrilaterals. Let's denote the side length of the base as s. Since the base is a regular quadrilateral, we can find the area of one base as A_base = s^2.

The total lateral area of the prism, AL, is given as AL = 624 cm^2. Since a quadrilateral prism has two congruent bases, the lateral area is equal to the perimeter of the base multiplied by the height of the prism.

AL = Perimeter_base * h
624 = 4s * 13
624 = 52s
s = 12 cm

Thus, the area of one base is A_base = s^2 = 12^2 = 144 cm^2.

The surface area of the prism can be computed by summing the lateral area and the area of the two bases:

Surface Area = AL + 2 * A_base
Surface Area = 624 + 2 * 144
Surface Area = 912 cm^2

Therefore, the surface area of the prism is 912 cm^2.

2) Volume of the prism:
The volume of the prism can be found by multiplying the area of the base by the height:

Volume = A_base * h
Volume = 144 * 13
Volume = 1872 cm^3

Therefore, the volume of the prism is 1872 cm^3.

AL = 2(L*h) = 624cm^2.

2(L*13) = 624, L = 24cm.

Assuming the ends are square, W = h = 13 cm.

1. As = 2(L*W) + AL.
Or As = 2(L*W) + 2(L*h).

2. V = L*W*h.

Correction:

1. As = 2(L*W) + 2(L*h) + 2(W*h).

AL = 2(W*h) + 2(L*h) = 624cm^2.

2(13*13) + 2(L*13) = 624,
338 + 26L = 624,
L = 11 m.

1. Assuming the ends are square, W = h = 13 m.

As = 2(L*W) + 2(L*h) + 2(W*h).

2. V = L*W*h.

The prism is regular, meaning its bases are squares, of side s. Now you know that

h=13
4sh = 624
So, s = 12

Now you can work out the rest.