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find the total surface area of this triangular prism 21cm 29cm 20cm 22cm

Find The Total Surface Area Of This Triangular Prism 21cm 29cm 20cm 22cm class=

Sagot :

lcyHot

Total surface area -

  • 2(1/2 × 20 × 21) + (29 × 22) + (21 × 22) + (20 × 22)

  • 420 + 638 + 462 + 440

  • 1960 cm²
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Answer:

[tex]\huge\boxed{SA=1960cm^2}[/tex]

Step-by-step explanation:

We have:

  • 2 rectangular triangles with legs 20cm and 21cm
  • 3 different rectangles 20cm × 22cm, 21cm × 22cm and 29cm × 22cm

The formula of an area of

  • a rectangular triangle:

[tex]A_\triangle=\dfrac{a\cdot b}{2}[/tex]

a, b - legs

  • a rectangle a × b:

[tex]A_{\square}=a\cdot b[/tex]

Calculate:

Rectangular triangle

[tex]A_\triangle=\dfrac{20\cdot21}{2}=210(cm^2)[/tex]

Rectangles:

[tex]A_{\square1}=20\cdot22=440(cm^2)\\\\A_{\square2}=21\cdot22=462(cm^2)\\\\A_{\square3}=29\cdot22=638(cm^2)[/tex]

Total surface:

[tex]SA=2A_\triangle+A_{\square1}+A_{\square2}+A_{\square3}\\\\SA=2\cdot210+440+462+638=1960(cm^2)[/tex]

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