Question

Use formulas to find the lateral area and surface area of the given prism. Round your answer to
the nearest whole number. The figure is not drawn to scale. The bases are right triangles.
8.94 m
4m
8m
41 m

Answer 1

Answer:

The answer is option B

$859$ $m^2$ $,$ $891$ $m^2$

Step-by-step explanation:

Step 1

Find the lateral area

we know that

The formula to calculate the lateral area is equal to

$LA=Ph$

where

P is the perimeter of the base of the prism

h is the height of the prism

In this problem we have

$P=4+8+8.94=20.94$ $m$

$h=41$ $m$

substitute in the formula

$LA=20.94*41=858.54$ $m^2$

$LA=859$ $m^2$

Step 2

Find the surface area

we know that

The formula to calculate the surface area is equal to

$SA=2B+Ph$

where

B is the area of the base of the prism

P is the perimeter of the base of the prism

h is the height of the prism

In this problem we have

$B=8*4/4=8$ $m^2$

$P=4+8+8.94=20.94$ $m$

$h=41$ $m$

substitute in the formula

$SA=4(8)+20.94*41=890.54$ $m^2$

$SA=891$ $m^2$