Top of the tower
The top of the tower has the shape of a regular hexagonal pyramid. The base edge has a length of 1.2 m. The pyramid height is 1.6 m. How many square meters of sheet metal are needed to cover the top of the tower if 15% extra sheet metal is needed for joints, overlap, and waste?
Correct answer:
Showing 2 comments:
Mathematican
We need to find the apothem (a) of the base first, so then you can find the height of a triangle of the face since you don't have this, just the height of the pyramid.
0.62 + a2 = 1.22 then this a is the apothem, and you can use to find the height of "triangle a face". So h2 2 = 1.62 + a2. And now you do what it is written with these new values.
0.62 + a2 = 1.22 then this a is the apothem, and you can use to find the height of "triangle a face". So h2 2 = 1.62 + a2. And now you do what it is written with these new values.
Mathematican
Thank Luiza. We just corrected this pyramid problem. So h is the height of the whole pyramid, h2 is wall height and h1 is now the height of the base triangles (hexagon is composed of six equilateral triangles).
Tips for related online calculators
You need to know the following knowledge to solve this word math problem:
- algebra
- expression of a variable from the formula
- solid geometry
- pyramid
- surface area
- planimetrics
- Pythagorean theorem
- right triangle
- polygon
- triangle
Units of physical quantities:
Grade of the word problem:
Related math problems and questions:
- The number 10
The number of sides of two regular polygons differ by 1 the sum of the interior angles of the polygons is in the ratio of 3:2 calculate the number of sides of each polygon. - The apothem
The apothem of a regular hexagon is 5√3 inches. Find one of its sides and area. - One side 4
One side of a regular octagon is 12 inches. Find the apothem and its area. - The interior
The interior angle of a regular polygon is x. If x is 9° less than the average of 153° and 145°, find the number of sides of the polygon. - Regular polygons
Two regular polygons, x and y, are such that the number of sides of x is three more than the number of the sides of y. If the sum of the exterior angles of x and y is 117°, how many sides have x? - Interior angles - sum
For the sum s of the interior angles of a polygon, where n is the number of its sides, the relation s=(n−2)⋅180 degrees applies. How many sides does a polygon have if the sum of its interior angles is 900°? - Goat
The fenced flower bed has the shape of a regular hexagon. The tops are formed by fence posts. The fence around the flowerbed measures 60 m. A goat is tied to one of the pillars from the outside and grazes on the surrounding meadow (the goat should not ent - Carousel for children
There are 5 seats evenly distributed on the children's carousel in the shape of a circle. What kind the arm of the carousel (connecting the center of the carousel to the seat) is long if the distance between with two seats is 1.2m? - Seats on carousel
There are 12 seats evenly distributed on the children's carousel in the shape of a circle. How long is the arm of the carousel (connecting the center of the carousel to the seat) if the distance between the two seats is 1.5m? - Angles of a hexagon
Find the interior angles of a hexagon if the sizes of the angles form an arithmetic sequence, and the smallest angle is 70°. - A dodecagon
Find the surface area of a regular 12-sided polygon if its side is a = 12 cm. - Inscribed and described circle
Find the radii of a circle inscribed and circumscribed by a regular pentagon whose side measures 3 cm. - Quadrilateral 27693
Construct a quadrilateral ABCD with diagonals AC = e = 7cm, BD = f = 6.2cm, d = 4.3cm, a = 5.3cm and β = 125° - Pentadecagon
Calculate the area of a regular 15-sides polygon inscribed in a circle with a radius r = 4. Express the result to two decimal places. - Dodecagon
Calculate the size of the smaller angles determined by lines A1 A4 and A2 A10 in the regular dodecagon A1A2A3. .. A12. Express the result in degrees. - Interior angles
In a quadrilateral ABCD, whose vertices lie on some circle, the angle at vertex A is 58 degrees, and the angle at vertex B is 134 degrees. Calculate the sizes of the remaining interior angles. - Pentagonal prism
The regular pentagonal prism is 10 cm high. The radius of the circle of the described base is 8 cm. Calculate the volume and surface area of the prism.