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what are they?
on these three i need to find the surface area
for the first one we have 4 triangles and a square. the area of a triangle is .5(base)(height) and the area of a square is (base)^2
so we have 4(.5)(base)(height)+b^2
well i redid the first one and i got 103.47
=2(base)(height)+(base)^2=2(4.2)(10)+(4.2)^2 is this what you did?
I got 101.64
oh yeah that's what i meant..
the second we have 4 triangles
so we have 4 times .5(b)(h) since there are all congruent triangles
it looks like you got a check mark on that one and the answer was 67.5?
yea.. all the ones i post need fixed
does everything make sense so far?
ok lets look at the last one
6 times .5bh
yes there are 6 triangles and then there is that hexagon hex means 6 right?
lets look at the triangles first the base 6 and we need to find the height
thats if we look at one traingle
if we divide a triangle and half we can from a right triangle so we can use the Pythagorean thm the hyp is 12 and if we divide the base in half the base is 3 or our newly formed triangle so we can find the height of the triangle let's call it h. we have 3^2+h^2=12^2 implies h=sqrt(135). so the area of the whole traingle is .5(6)(sqrt(135) since we have 6 trangles we have this area times 6 so this equals 18(sqrt(135)) but now we need to find the area of the hexagon
if we draw two vertical lines from one vertex to another and one horizontal line from one vertex to another we would form 2 rectangles and 4 traingles
looking at one triangle we see that the hyp is 6 and we know that the legs are equal. so we have b^2+b^2=6^2 imples 2b^2=36 implies b^2=18 implies b=sqrt(18) so the area of the triangle is .5(sqrt18)(sqrt(18)=.5(18)=9 since we have 4 of these triangles then we multiply the 9 by 4 =36 now we need to find the area of the rectangles we know 1 side =6 so we need find the length of the other side that runs perpendicular to it
but we found that when we were finding the legs of the triangle above so the side running perpendicular to the 6cm side has length sqrt(18) so the area of the rectangle is (6)sqrt(18) but since we have 2 we multiply by 2 giving us 12sqrt(18) now we add all of our areas together
so we have the area of the 6 triangles is 18sqrt(135) and we have the area of the hexagon is 12sqrt(18)+36 the total surface area is 18sqrt(135)+12sqrt(18)+36
i got 296.05
i did my math wrong..
but thank u
that last problem was really long I hope i'm right lol
can help me with some more
more surface area?
ok i will look at one more and then i have to leave
ok the first one we need to find the area of the base and multiply by the height of the solid
the area of the base is .5(b)(h)=.5(6)(8)=24 the height of the solid is 10 so 24(10)=240
the second one you shouldnt had divided by 3 it should had been 2
the last one you set it up right but you should had got 3451.04
okay thank you
np i hope i was a help