Question

What is the total area of the triangular prism in square cm?10cm

Answer 1

Step-by-step explanation

We are to find the total area of the triangular prism

To do so, we will have to split the triangle into 5 parts labeled A, B, C. D, and E as shown below

The total area of the prism is the area of the individual parts

For part A, we will have to get the other dimension of the base

We will get x using the Pythagoras theroem

`x^=√(10^2-6^2)=√(100-36)=√(64)=8`

The value of x is 8

So we can now proceed to get the areas as follow

Part A

`Area\text{ of triangle}=(1)/(2)*8*6=24cm^2`

Part B and part A are similar, they have the same area

So area of part B = part A = 24 cm²

For part E

Area is

`Area\text{ of rectangle =length}* breadth=22*8=176cm^2`

For part D

Area of rectangle is length x breadth =

`10cm*22cm=220cm^2`

Part C

Area is given as length x breadth

`6cm*22cm=132cm^2`

So, we will sum all the areas to find the total area to be

`24+24+176+220+132=576cm^2`

Thus, the area of the triangular prism is 576cm²