Question

What is the total surface area

Answer 1

We have two right triangles and three different rectangles.

The formula of an area of a right triangle:

`A_T=(1)/(2)l_1l_2`

l₁, l₂ - legs

We have l₁ = 20cm and l₂ = 21cm. Substitute:

`A_T=(1)/(2)(20)(21)=(10)(21)=210\ cm^2`

The formula of an area of a rectangle:

`A_R=lw`

l - length

w - width

We have:

rectangle #1: l = 22cm, w = 29cm

`A_(R1)=(22)(29)=638\ cm^2`

rectangle #2: l = 22cm, w = 21cm

`A_(R2)=(22)(21)=462\ cm^2`

rectangle #3: l = 22cm, w = 20cm

`A_(R3)=(22)(20)=440\ cm^2`

The total Surface Area of the triangular prism:

`S.A.=2A_T+A_(R1)+A_(R2)+A_(R3)\\\\S.A.=2\cdot210+638+462+440=1960\ cm^2`