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the surface area of a right triangular prism is 228 square inches. The base is a right triangle with a base height of 6 inches and a base length of 8 inches. The length of the third side of the bae is 10 inches. Find the height of the prism.



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Sagot :

[tex]look\ at\ the\ picture\\\\Area=228\ in^2\\\\Area=2A_1+A_2+A_3+A_4\\\\2A_1=2\cdot\frac{6\cdot8}{2}=48\ (in^2)\\\\A_2=8H\\\\A_3=6H\\\\A_4=10H[/tex]

[tex]48+8H+6H+10H=228\\\\48+24H=228\ \ \ /-48\\\\24H=180\ \ \ /:24\\\\H=7.5\ (in)[/tex]
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Answer:

The height of right triangular prism is 7.5 in.

Step-by-step explanation:

The base is a right triangle with a base height of 6 inches and a base length of 8 inches. The length of the third side of the base is 10 inches.

The area of a triangle is

[tex]A=\frac{1}{2}\tims base\times height[/tex]

[tex]A_1=\frac{1}{2}\tims 6\times 8=24[/tex]

Let the height of the prism be h.

Area of a rectangle is

[tex]A=length\times width[/tex]

[tex]A_2=6\times h=6h[/tex]

[tex]A_3=8\times h=8h[/tex]

[tex]A_4=10\times h=10h[/tex]

The surface area of a right triangular prism is

[tex]A=2\times \text{Area of base}+\text{Area of three rectangles}[/tex]

[tex]A=2\times (A_1)+A_2+A_3+A_4[/tex]

[tex]A=2\times (24)+6h+8h+10h[/tex]

[tex]A=48+24h[/tex]

The surface area of a right triangular prism is 228 square inches.

[tex]228=48+24h[/tex]

[tex]180=24h[/tex]

[tex]h=7.5[/tex]

Therefore the height of right triangular prism is 7.5 in.

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