Mathematics: List and descripe the steps you would use to model 7/10_4/10

List and descripe the steps you would use to model

sarahhtsvetkovs

22.10.2022

$A = 144\ cm^{2}$

Step-by-step explanation:

Let A be the surface area of the triangular prism

Given:

A triangular prism

Height $h = 4\ cm$

Base $b = 8\ cm$

Perimeter of the base triangle (p = 6 + 8 + 10 = 24 cm)

Now we calculate the surface area of the triangular prism.

Solution:

We know that the surface area of the triangular prism.

$Surface\ Area = Lateral Area + 2(Base\ Area)$

$A = A_{L} + 2(A_{B})$ -------------(1)

First We calculate the lateral surface area of the triangular prism.

$Lateral\ surface\ area = Perimeter\ of\ the\ base\ triangle\times Height$

$A_{L} = p\times h$

Perimeter of the base and height are known, so we substitute these value in above equation.

$A_{L} = 24\times 4$

$A_{L} = 96\ cm^{2}$

Therefore the lateral surface area of the triangular prism $A_{L} = 96\ cm^{2}$

Now we calculate area of the base.

$Area\ of\ base = \frac{1}{2}bh$

Where b = base and h = Height are known.

$Area\ of\ base = \frac{1}{2}\times 8\times 6$

$Area\ of\ base = 4\times 6$

$Area\ of\ base = 24\ cm^{2}$

So the area of the base $A_{B) = 24\ cm^{2}$

Substitute Lateral surface area and base area in equation 1.

A = 96 + 2(24)

A = 96 + 48

$A = 144\ cm^{2}$

Therefore the surface area of the triangular prism $A = 144\ cm^{2}$

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