Answer:
55.5 square feet
Step-by-step explanation:
so the dog house consists of 4 walls, two roof sections, and two triangle bits to make the roof pointy (I'm sure they have a name but I don't know what it is lol) Of the walls there would be 2 of the longer walls and 2 of the shorther ones. Knowing this we just have to add together the area of each part to find the total surface area.
So starting with the walls:
two of them are 4 feet by 2 feet.
The area of a rectangle is just length x width
so those two would have an area of 8 ft^2
and the other two are 3 feet by 2 feet so they would have an area of 6 ft^2
the roof sections are also rectangles with dimensions of 4 feet by 2.5 feet
4x2.5=10 so each side of the roof has a surface area of 10 ft^2
now the triangle parts have a base of 3 feet and a height of 2.5 feet
the formula for area of a triangle is base x height / 2
3x2.5=7.5
7.5/2= 3.75
now we add them together
8+8+6+6+10+10+3.75+3.75=55.5
so the total surface area is 55.5 square ft
Answer:
{(5, –4), (–4, 5), (–5, 4), (4, –5)}
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V=LWH
W=2
120=V
120=L2H
divide by 2
60=LH
SA
2 pairs of same sides
1 bottom
SA=2(LH+WH)+LW
we know that W=2 so
SA=2(LH+2H)+2L
exanded
SA=2LH+4H+2L
we need to solve for 1 variable to eliminate it
60=LH
divide both sides by L
60/L=H
sub 60/L for H
SA=2L(60/L)+4(60/L)+2L
SA=2(60)+(240/L)+2L
SA=120+(240/L)+2L
SA=184
184=120+(240/L)+2L
multiply both sides by L
184L=120L+240+2L²
minus 184L both sides
0=2L²-64L+240
factor
0=2(L²-32L+120)
use quadratic formula
L=16-2√34 or 16+2√34
the dimentions are (aprox)
Legnth=4.3381, Width=2, Height=13.831 or
Legnth=27.6619, Width=2, Height=2.1691
