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.

A. 951 m²; 958 m²
B. 951 m²; 969 m²
C. 940 m²; 958 m²
D. 940² m; 969 m²

Answer 1

Lateral area around don't count the ends that are triangle
Bottom is 9 times 47= 423
Right side 9.23 times 47= 433.81
Left side 2 times 47= 94
Total lateral area = 950.81

Triangles 1/2 (9)(2)(2)=18
Total surface area= 968.81

Answer 2

The answer is the option B

`951\ m^(2), 969\ m^(2)`

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=2+9+9.23=20.23\ m`

`h=47\ m`

substitute in the formula

`LA=20.23*47=950.81\ m^(2)`

`LA=951\ 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=9*2/2=9\ m^(2)`

`P=2+9+9.23=20.23\ m`

`h=47\ m`

substitute in the formula

`SA=2(9)+20.23*47=968.81\ m^(2)`

`SA=969\ m^(2)`