The Pyramid is an arena in Memphis, Tennessee. Its height is 321 ft., and its slant height is 436.5 ft. Find the length of the edge of the square base. Round the answer to the nearest tenth.
591.6
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Given l=30 in. , w=20 in. , h=18 in. , and x=36.1 in. , find the length of d . Round the answer to the nearest tenth.
(1 point)
For the square pyramid, the lateral edge length, e , is 25 in., and the slant height, s , is 24 in. Find the height of the pyramid, h . Round the answer to the nearest whole number. Hint: Before finding the length of h , you will first need to find the length of r
.
(1 point)
The height of the square pyramid is
what is 36.1 in rounded to the nearest tenth
36.1 inches rounded to the nearest tenth would be 36.1 inches itself, since it is already rounded to the nearest tenth.
295.8
Apologies for the mistake. Let's recalculate it correctly:
Using the Pythagorean theorem, we have:
x^2 + (321 ft.)^2 = (436.5 ft.)^2
x^2 + 103041 ft.^2 = 190512.25 ft.^2
x^2 = 190512.25 ft.^2 - 103041 ft.^2
x^2 = 87471.25 ft.^2
Taking the square root of both sides, we get:
x = √87471.25 ft.^2 ≈ 295.7 ft.
Therefore, the length of the edge of the square base of the Pyramid is approximately 295.7 ft. (rounded to the nearest tenth).
To find the height of the square pyramid, we need to find the length of the vertical height of the pyramid.
We can use the Pythagorean theorem to relate the height, slant height, and the length of the lateral edge.
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
Let's call the height of the pyramid "h" and the length of the slant height "s". The length of the lateral edge is given as "e".
Using the Pythagorean theorem, we have:
h^2 + r^2 = s^2
Since the lateral edge length is given as 25 inches, and it connects the midpoint of the base to the vertex, we know that the lateral edge divides the base into two congruent right triangles. Half of the base, which is a side of the right triangle, is equal to r/2.
So, we can rewrite the equation as:
h^2 + (r/2)^2 = s^2
Substituting the given values, we have:
h^2 + (25/2)^2 = 24^2
Simplifying the equation, we get:
h^2 + 625/4 = 576
Multiplying both sides by 4 to remove the fraction, we have:
4h^2 + 625 = 2304
Subtracting 625 from both sides, we get:
4h^2 = 1679
Dividing both sides by 4, we have:
h^2 = 419.75
Taking the square root of both sides, we get:
h = √419.75
Calculating the square root of 419.75, we get:
h ≈ 20.5
Therefore, the height of the square pyramid is approximately 20.5 inches when rounded to the nearest whole number.
To find the length of d, we need to use the Pythagorean theorem.
d is the hypotenuse of a right triangle formed by l, w, and d.
Using the Pythagorean theorem, we have:
d^2 = l^2 + w^2
Substituting the given values, we have:
d^2 = 30^2 + 20^2
d^2 = 900 + 400
d^2 = 1300
Taking the square root of both sides, we have:
d ≈ √1300
Calculating the square root of 1300, we get:
d ≈ 36.06
Therefore, the length of d is approximately 36.1 inches when rounded to the nearest tenth.
Apologies for the mistake. Let's recalculate it correctly:
Using the Pythagorean theorem, we have:
d^2 = l^2 + w^2
Substituting the given values, we have:
d^2 = 30^2 + 20^2
d^2 = 900 + 400
d^2 = 1300
Taking the square root of both sides, we have:
d ≈ √1300
Calculating the square root of 1300, we get:
d ≈ 36.06
Therefore, the length of d is approximately 36.1 inches when rounded to the nearest tenth.
Apologies for the confusion. Let's calculate it correctly:
Using the Pythagorean theorem, we have:
x^2 + (321 ft.)^2 = (436.5 ft.)^2
x^2 + 103041 ft.^2 = 190522.25 ft.^2
x^2 = 87481.25 ft.^2
Taking the square root of both sides, we get:
x ≈ √87481.25 ft.^2 ≈ 295.6 ft.
Therefore, the length of the edge of the square base of the Pyramid is approximately 295.6 ft. (rounded to the nearest tenth).
To find the length of the edge of the square base of the Pyramid in Memphis, Tennessee, we can use the Pythagorean Theorem.
The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the height of the pyramid is the perpendicular side, and the slant height is the hypotenuse.
Let's call the length of the edge of the square base of the pyramid "x". We can now set up the equation using the Pythagorean Theorem:
x^2 + 321^2 = 436.5^2
Simplifying the equation, we have:
x^2 = 436.5^2 - 321^2
x^2 = 190,622.25 - 103,041
x^2 = 87,581.25
To find the square root of both sides of the equation to get the value of "x," we have:
x = √87,581.25
Calculating the square root of 87,581.25, we get:
x ≈ 295.9
Therefore, the length of the edge of the square base of the Pyramid in Memphis, Tennessee, is approximately 295.9 feet when rounded to the nearest tenth.
Apologies for the incorrect calculation. Let's try again:
Using the Pythagorean theorem, we have:
x^2 + (321 ft.)^2 = (436.5 ft.)^2
x^2 + 103041 ft.^2 = 190512.25 ft.^2
x^2 = 87471.25 ft.^2
Taking the square root of both sides, we get:
x ≈ √87471.25 ft.^2 ≈ 295.5 ft.
Therefore, the length of the edge of the square base of the Pyramid is approximately 295.5 ft. (rounded to the nearest tenth).
To find the length of the edge of the square base, we can use the Pythagorean theorem.
Let's call the length of the edge of the square base x. According to the Pythagorean theorem, we have:
x^2 + (321 ft.)^2 = (436.5 ft.)^2
Simplifying the equation, we get:
x^2 + 103041 ft.^2 = 190523.25 ft.^2
Subtracting 103041 ft.^2 from both sides, we get:
x^2 = 87482.25 ft.^2
Taking the square root of both sides, we get:
x ≈ √87482.25 ft.^2 ≈ 295.7 ft.
Therefore, the length of the edge of the square base of the Pyramid is approximately 295.7 ft. Rounded to the nearest tenth, the length is 295.7 ft.
To find the length of the edge of the square base, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (in this case, the slant height) is equal to the sum of the squares of the other two sides.
Let's call the length of the edge of the square base "x". We can form a right triangle using the height, slant height, and the edge of the square base. The height would be one leg of the triangle, the slant height the hypotenuse, and the edge of the square base the other leg.
Using the Pythagorean theorem, we have:
x^2 + 321^2 = 436.5^2
x^2 + 103041 = 190512.25
x^2 = 87471.25
Taking the square root of both sides, we get:
x = √87471.25
x ≈ 295.7
Therefore, the length of the edge of the square base is approximately 295.7 ft. (rounded to the nearest tenth).