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:

$A_T=\dfrac{1}{2}l_1l_2$

l₁, l₂ - legs

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

$A_T=\dfrac{1}{2}(20)(21)=(10)(21)=210\ cm^2$

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:

$S.A.=2A_T+A_{R1}+A_{R2}+A_{R3}\\\\S.A.=2\cdot210+638+462+440=1960\ cm^2$