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Find the surface area of the prism.8cm6cm13cm10cmSurface Area = [?]cm2

Find the surface area of the prism.8cm6cm13cm10cmSurface Area = [?]cm2-example-1

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The prism of the picture has 5 faces. 2 triangles and 3 rectangles.

The 2 triangles are equal (top and bottom of the prism), with a base of 8cm and a height of 6cm.

The rectangle of the front has a base of 10cm and a height of 13 cm.

The rectangle of the back has a base of 8cm and a height of 13cm.

The rectangle of the left has a base of 6cm and a height of 13cm.

To find the surface area of the prism, we need to find the area of each of those 5 faces, and finally sum them.

The area of the both triangles can be calculated as half the product between base and height:


A_(trangle)=(b\cdot h)/(2)

Recalling the dimensions of both triangles (8cm of base and 6cm of height), the area will be:


A_(trangle)=\frac{(8cm)\cdot(6\operatorname{cm})}{2}=(48)/(2)cm^2=24\operatorname{cm}

The area of both triangles is 24 square centimeters. We need to keep in mind that in the final sum we need to add this area twice, since there are 2 triangles.

The area of the front rectangle is just the product between base and height:


A_(rect-front)=b\cdot h=(10\operatorname{cm})\cdot(13\operatorname{cm})=130\operatorname{cm}

The same for the rectangle of the back:


A_(rect-back)=b\cdot h=(8\operatorname{cm})\cdot(13\operatorname{cm})=104\operatorname{cm}

And finally, the same for the left rectangle:


A_(rect-left)=b\cdot h=(6\operatorname{cm})\cdot(13\operatorname{cm})=78\operatorname{cm}

Now we have the area of each of the 5 faces of the prism. To find the surface area we need to sum all of them. Remember the area of the triangle will be added twice:


A=2A_(trangle)+A_(rect-front)+A_(rect-back)+A_(rect-left)
\begin{gathered} A=2\cdot24\operatorname{cm}+130\operatorname{cm}+104\operatorname{cm}+78\operatorname{cm}^2 \\ A=48\operatorname{cm}+130\operatorname{cm}+104\operatorname{cm}+78\operatorname{cm} \end{gathered}

Finally:


A=360\operatorname{cm}^2

The surface area of the prism is 360 square centimeters.

User Rishi Dwivedi
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