Question

What is the surface area of the composite figure?
~Attachment in comments~

Answer 1

Take it in pieces and sum up the values at the end. It's going to be:\[SA_{bottom}+4SA_{side}+4SA_{triangle~side}\]

Answer 2

If you're stumped on this let me know and I'll walk you through it.

Answer 3

It would help if you could walk me through it, please?

Answer 4

Ok, the bottom of the figure is a square with 6mm sides right? Well, the SA of a square is just side*side: \[6mm*6mm=36mm^2\]

Answer 5

The sides are rectangles so it's basically SA = LW:\[7mm*6mm=42mm^2\]

Answer 6

The top parts are just triangles with a 6mm base and a height of 4mm. The SA of a triangle is (1/2)bh:\[\frac{(6mm)(4mm)}{2}=12mm^2\]

Answer 7

Now use the first equation I posted which sums it all up to get the total surface area. If you work it out I'll double-check your answer.

Answer 8

For some reason I've got 90 mm^2 but that's not even close to one of the answers I have :/

Answer 9

I think I lost you...here:\[SA_{total}=SA_{bottom}+4SA_{side}+4SA_{triangle~side}\]\[SA_{total}=36+4(42)+4(12)=?\]

Answer 10

There's no magic formula when doing these types of problems. You just take the individual areas and sum them up at the end.

Answer 11

252 mm^2?

Answer 12

Yes

Answer 13

Thank you!

Answer 14

yw, good luck :)