Question

Use the given information to determine the lateral and surface areas of thesolid. Round your answer to the nearest unit.

Answer 1

`\begin{gathered} \text{Lateral = 96 in}^2 \\ \text{Total = 108 in}^2 \end{gathered}`

Here, we want to use the given information to calculate the lateral and the total surface area

To find the lateral area, we have to calculate the perimeter of the base and multiply this by the height of the triangular prism

Now, we will make the shape lie on its side

This mean the triangles will represent the base

Mathematically, the perimeter of a triangle is the sum of its side

We need the last side of the triangle

We can get this by the use of Pythagoras' theorem

As we can see, the side measure 5 is the hypotenuse as it faces the right angle

The square of the hypotenuse equals the sum of the squares of the two other sides

3,4 and 5 are a Pythagorean triple

This means that, the measure 3 is the last side of the triangle

So the perimeter is;

`3+4+5\text{ = 12 in}`

The height is the measure 8 inches

Thus, the lateral area is;

`12\text{ }*8=96in^2`

Now, we want the total surface area, but firstly, we need the area of the base

The area of the base is the area of the triangle

`\begin{gathered} B\text{ = }(1)/(2)* b* h \\ \\ B\text{ = }(1)/(2)*4*3=6in^2 \end{gathered}`

two times this is 12 in^2

The total suface area is thus;

`96in^2+12in^2=108in^2`