Jillian wants to find the surface area of a pyramid the base is a square with sides that are 4 inches long the other faces are i
sosceles triangles the ratio of the height of each triangle to its base is 3:1
part a: give the Base length and the height of each triangular face
part b : find the combined area of the Triangular faces
part c: find the surface area of the pyramid
part a: give the Base length and the height of each triangular face
part b : find the combined area of the Triangular faces
part c: find the surface area of the pyramid
2 answers:
Check the picture below.
so the pyramid is more or less like so, keep in mind that the base of it is a square, thus is called a "square" pyramid.
a)
since the height : base are on a 3:1 ratio, namely the height is three times as large as the base, if the base of a triangular face is 4, then the height is 3(4), as you see there.
b)
there are 4 triangles, recall that A = 1/2 bh, thus
![\bf \stackrel{\textit{area of the four triangles}}{4\left[ \cfrac{1}{2}(4)(12) \right]}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7B%5Ctextit%7Barea%20of%20the%20four%20triangles%7D%7D%7B4%5Cleft%5B%20%5Ccfrac%7B1%7D%7B2%7D%284%29%2812%29%20%5Cright%5D%7D)
c)
well, you already know the lateral area, namely the area of the four triangles, the total surface area is just that plus the area of the base, well, the base is just a 4x4 square, so add that to the triangle's area, and that's the total surface area.
so the pyramid is more or less like so, keep in mind that the base of it is a square, thus is called a "square" pyramid.
a)
since the height : base are on a 3:1 ratio, namely the height is three times as large as the base, if the base of a triangular face is 4, then the height is 3(4), as you see there.
b)
there are 4 triangles, recall that A = 1/2 bh, thus
c)
well, you already know the lateral area, namely the area of the four triangles, the total surface area is just that plus the area of the base, well, the base is just a 4x4 square, so add that to the triangle's area, and that's the total surface area.
Answer:
a.Length of base=4 inches
Length of height=12 inches
b.Area of triangular faces=96 square inches
c.Surface area of pyramid=112 square inches
Step-by-step explanation:
We are given that base of pyramid is square shaped with side 4 inches long
Other faces are isosceles triangles
We are given that ratio of height of each triangle to its base =3:1
a.We have to find the length of base and the height of each triangular face
Length of base=4 inches
Height is 3 times the base
Therefore, length of height=
b.There are 4 triangular faces
We know that area of triangle=
Using this formula
Area of one triangular face ==24 square inches
Area of 4 triangular faces=
c. Surface area of pyramid=area of 4 triangular faces+area of square
Surface area of pyramid =
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Answer/Step-by-step explanation:
Equation to represent the daily rental cost for each type of truck can be written as follows:
Daily rental cost for Trucks-A-Lot = 42 + 0.72m
Daily rental cost for Move-in-Truckers = 70 + 0.12m
Where, m = Emily's mileage
To determine the number of miles for which the truck cost the same amount, set both equations equal to each other and solve for m.
Collect like terms
Divide both sides by 0.6
At approximately 47 miles, both trucks would cost the same amount.
Check:
Daily rental cost for Trucks-A-Lot = 42 + 0.72m
Plug in the value of x = 47
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Daily rental cost for Move-in-Truckers = 70 + 0.12m
Plug in the value of x = 47
= 70 + 0.12(47) = $75.64 ≈ $76