A chocolate box made of cardboard is in the shape of a triangular prism. The prism's bases are isosceles triangles. The chocolate box has a decorative paper wrapper covering only its rectangular sides. A net of the chocolate box is shown below. How much decorative paper and cardboard are needed for the chocolate box, to the nearest hundredth of a square inch? Decorative paper: 30.5 in2; cardboard: 37.4 in2 Decorative paper: 30.5 in2; cardboard: 33.95 in2 Decorative paper: 34.5 in2; cardboard: 37.95 in2 Decorative paper: 34.5 in2; cardboard: 41.4 in2

triangular prism - Chegg

The Chocolate Box Has A Decorative Paper Wrapper Covering Only Its Rectangular Sides. A Net Of The Chocolate Box Is Shown Below 1.5 In 1.9 In 1.9 In 2.3 In 5 In 1.5 In How Much Decorative Paper And Cardboard .

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .