Which could be the area of one face of the triangular prism? Select three options.

A triangular prism. The rectangular sides are 12 by 10, 12 by 8, and 12 by 6. The triangular sides have a base of 8 and height of 6.
[Not drawn to scale]
24 square units
48 square units
72 square units
96 square units
144 square units

(A)24 square units

(C)72 square units

(D)96 square units

Step-by-step explanation:

Triangular face

Height of the Triangle=6 Units

Base of the Triangle=8 Units

Area of the Triangular Face

Rectangular Faces

Area of Rectangular face with dimension 12 by 10=12 x 10=120 Square Units

Area of Rectangular face with dimension  12 by 8= 12 X 8=96 Square Units

Area of Rectangular face with dimension 12 X 6=12 x 6=72 Square Units

From the options, the areas are:

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

equation image indicator

x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

equation image indicator

x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

equation image indicator

x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!