Question

Part B if the height of each prism is 10 Cm what is the surface area prism

Answer 1

Answer:

Prism A:

$Area = 288cm^2$

Prism B:

$Area =250cm^2$

Step-by-step explanation:

Given

See attachment for prisms

$Height(h) = 10cm$

Required

Determine the surface area of both prisms

Prism A is triangular and as such, the surface area is:

$Area = 2 * A_b + (a + b + c) * h$

Where

$A_b = \sqrt{s * (s - a) * (s -b) * (s - c)}$

and

$s = \frac{a + b + c}{2}$

Such that a, b and c are the lengths of the triangular sides of the prism.

From the attachment;

$a = 8; b =6; c =10$

So, we have:

$s = \frac{a + b + c}{2}$

$s = \frac{8 + 6 + 10}{2}$

$s = \frac{24}{2}$

$s = 12$

Also:

$A_b = \sqrt{s * (s - a) * (s -b) * (s - c)}$

$A_b = \sqrt{12 * (12 - 8) * (12 - 6) * (12 - 10)}$

$A_b = \sqrt{576}$

$A_b = 24$

So:

$Area = 2 * A_b + (a + b + c) * h$

$Area = 2 * 24 + (8 + 6 + 10) * 10$

$Area = 288cm^2$

Prism B is a rectangular prism. So, the area is calculated as:

$Area = 2 * (ab + bh + ah)$

From the attachment

$a = b = 5$

$h =10$

So:

$Area =2 * (5 * 5 + 5 * 10 + 5 * 10)$

$Area =250cm^2$