What is the surface area of the right prism below?

Surface area of the right prism =  156 square units

Step-by-step explanation:

Surface area of prism = area of 2 triangle + area of three rectangles

To find the area of triangles

Here base b = 4 units and height h = 3 units

Area of triangle = bh/2

 = (4 * 3)/2 = 6  square units

Area of 2 rectangles = 2 * 6 = 12 units

To find the area of rectangles

length of rectangle = 12 units,

Here 3 rectangles with 3 different width

width1 = √(4² + 3²) = 5 units

width2 = 4 units and width3 = 3 units

Area1 = Length * width1

 = 12 * 5 = 60 square units

Area1 = Length * width2

 = 12 * 4 = 48square units

Area1 = Length * width3

 = 12 * 3 = 36 square units

Total area of three rectangles = 60 + 48 + 36 = 144

To find the surface area of prism

Surface area = Area of triangles + area of rectangles

 = 12 + 144 = 156 square units

c

step-by-step explanation:

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

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