Which equation can be used to calculate the surface area of the triangular prism net show below?

The net of a rectangular prism. The rectangular sides are 10 centimeters by 13 centimeters, 10 centimeters by 12 centimeters, and 10 centimeters by 5 centimeters. The triangular sides have a base of 5 centimeters and height of 12 centimeters.

[Not drawn to scale]

Surface Area = (one-half) (5) (12) + (5) (10) + (12) (10) + (13) (10)
Surface Area = (one-half) (5) (13) + (one-half) (5) (13) + (13) (10) + (12) (10)
Surface Area = (2) (5) (13) + (5) (10) + (13) (10) + (12) (10)
Surface Area = (one-half) (5) (12) + (one-half) (5) (12) + (5) (10) + (12) (10) + (13) (10)

Given:

Net of a triangular prism

To find:

Which equation can be used to calculate the surface area of the triangular prism.

Solution:

Using formulas:

Area of rectangle = length × width

Area of triangle =

Area of left triangle =

Area of right triangle =

Area of bottom = 5 × 10

Area of Middle = 12 × 10

Area of top = 13 × 10

Surface area of triangular prism:

Surface area = Area of left triangle + Area of right triangle + Area of bottom + Area of middle + Area of top

Replace multiplication by brackets.

The equation can be used to calculate surface area of triangular prism is

.

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

you can first factor out the n to get n(1+5). we know that 1+5 is 6, so we just have 6n.