What is the slant height for the given pyramid to the nearest whole unit?
A pyramid with a rectangular base is shown. Inside is a blue triangle formed by vertices located at the center of the rectangular base, midpoint of a side of the base, and apex of the pyramid. Pyramid base = 10 cm
Height = 12 cm
A. 7 cm
B. 11 cm
C. 13 cm
D. 16 cm
To find the slant height of the pyramid, we need to use the Pythagorean theorem. The slant height is the hypotenuse of a right triangle formed by the height of the pyramid and half the length of the base.
Half the length of the base is 10/2 = 5 cm.
Using the Pythagorean theorem:
slant height = sqrt(5^2 + 12^2)
slant height = sqrt(169)
slant height ≈ 13 cm
Therefore, the slant height to the nearest whole unit is C. 13 cm.
To find the slant height of the pyramid, we can use the Pythagorean theorem.
Step 1: Find the base diagonal of the rectangular base. Since the base is a rectangle, we can use the Pythagorean theorem to find the length of the diagonal.
Using the formula c^2 = a^2 + b^2, where c is the diagonal and a and b are the sides of the rectangle, we have:
c^2 = 10^2 + 12^2
c^2 = 100 + 144
c^2 = 244
Taking the square root of both sides gives us:
c = √244
c ≈ 15.62 cm (rounded to two decimal places)
Step 2: Find the slant height of the pyramid. The slant height is the height of the blue triangle formed by the apex of the pyramid and the base and is also the height of one of the triangular faces of the pyramid.
Since the height of the pyramid is given as 12 cm, we can use the Pythagorean theorem again to find the slant height.
Using the formula c^2 = a^2 + b^2, where c is the slant height and a and b are the height and the base diagonal of the triangle, we have:
c^2 = 12^2 + 15.62^2
c^2 = 144 + 244
c^2 = 388
Taking the square root of both sides gives us:
c = √388
c ≈ 19.7 cm (rounded to one decimal place)
Therefore, to the nearest whole unit, the slant height of the pyramid is approximately 20 cm.
To find the slant height of the pyramid, we can use the Pythagorean theorem. The slant height is the hypotenuse of the right triangle formed by the height of the pyramid and half the length of the base.
Given:
Base length = 10 cm
Height = 12 cm
To find half the length of the base, divide the base length by 2:
Half the length of the base = 10 cm / 2 = 5 cm
Now, we can use the Pythagorean theorem to find the slant height:
Slant height^2 = Height^2 + (Half the length of the base)^2
Slant height^2 = 12 cm^2 + 5 cm^2
Slant height^2 = 144 cm^2 + 25 cm^2
Slant height^2 = 169 cm^2
Taking the square root of both sides, we get:
Slant height = √169 cm^2
Slant height = 13 cm
Therefore, the slant height of the pyramid is 13 cm.
The answer to the given question, to the nearest whole unit, is C. 13 cm.