Question

Use the figure below to answer the questions.

a. What is the name of the 3D shape?


b. What is the formula for total surface area for this shape?


c. What is the surface area of the figure?

Answer 1

a. What is the name of the 3D shape?

The name of the 3D shape is Prism

b. What is the formula for total surface area for this shape?

Total surface area:

`S=2A_(b)+P_(b)h`

c. What is the surface area of the figure?

The surface area of the figure is 144 cm²

Explanation:

a. What is the name of the 3D shape?

The 3D shape has two congruent and parallel faces (triangles) and the other faces are parallelograms, then the 3D shape is a prism

b. What is the formula for total surface area for this shape?

Total Surface area:

`S=2A_(b)+P_(b)h`

where:

Area of the base of the prism: Ab

Perimeter of the base: Pb

Height of the prism: h

c. What is the surface area of the figure?

The base of the prism is a triangle. Then to calculate the area of the base, we must use the formula to calculate the area of a triangle:

`A_(b)=(bh)/(2)\\ A_(b)=((4 cm)(3 cm))/(2)\\ A_(b)=(12cm^(2) )/(2)\\ A_(b)=6cm^(2)`

The perimeter of the base is the perimeter of the triangle, equal to the sum of the sides of the triangle:

`P_(b)=4cm+3cm+5cm\\ P_(b)=12cm`

h: Height of the prism is the distance between the bases of the prism (the triangle), then h=11 cm

Then, replacing in the formula the known values:

`S=2(6 cm^(2))+(12 cm)(11 cm)\\ S=12 cm^(2)+132 cm^(2)\\ S=144 cm^(2)`