I'm stuck on this math problem, please help ASAP! I'm at a loss of time and the help is very much appreciated.

Question

Find the volume and surface area of a triangular prism whose base is triangle of side lengths 60cm-50cm-50cm. and height 100cm.

Answer 1

First, you have to find the value of "s", which can then be inserted into:

Square Root of s(s - a)(s - b)( s - c)

The value of s comes from: SUM of three side lengths, then division by 2

This process will give you the entire area of the base (triangle) of this prism, at which point a person multiples the entire area of the base times the height of a prism in order to get the volume.

Thus, the three steps go as follows:

1.) "s" value: three side lengths: 60 + 50 + 50 = 160

divide that value by 2: 160/2 = 80 = "s value"

2.) use that "s" value in the square root equation given above, where a, b, c represent the three side lengths: s(s - a)(s - b)(s - c) = 80(80-50)(80-60)(80-50)

giving: 80(30)(20)(30) and after computing this value, square root!

80 times 30 times 20 times 30 is: 1,440,000

square root of 1,440,000 is: 1200

Thus, area of triangular base is 1200 square centimeters

3.) Last step!

Area of BASE times height will give volume of a prism

Area of base is 1200

so multiply that by height of 100 cm

and the final volume is: 120,000 with a label of cubic centimeters since this is volume.

Answer 2

The base is an isosceles triangle whose height is h² = 50² - 30² as the height splits the base (60) into two equal segments.

h² = 1600 ==> h = 40cm (the height of the base triangle)

VOLUME = BASE AREA x HEIGHT (PRISM)

V = 1/2 x 60 x 40 x 100 = 120000 cm³

SURFACE AREA = (2 x Area of the base triangle) + (Perimeter of the base triangle x Height of the prism)

Surface Area = ( 2 x 1/2 x 60 x 40 ) + ( 60 + 50 + 50 ) x 100

2400 + 16000 = 18400 cm^2