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Height of Pentagon = SideLength * (cos(18) + sin(36))
with angles measured in degrees
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If the sides of a pentagon equals x what is the height?
1.78x
Volume for a pentagon?
A pentagon is a two-dimensional geometric figure and therefore has area but not volume. To have volume, a geometric figure must have height or thickness as well as its plane dimensions.
What is the area of a regular pentagon if the radius r of the circumcircle is 3.4 cm and half the side length a is 2 cm rounded to 1 decimal place?
In a regular pentagon there are 5 vertices which connect to the circumcentre each a distance r = 3.4 cm away. This creates 5 triangles inside the pentagon; so the area of the pentagon is the sum of these five triangles; as the pentagon is regular, this is the same as 5 times the area of one of these triangles. The length of each side of the pentagon is twice half the length of one side → side = 2 × a = 2 × 2 cm Consider one side and the two radii connecting its ends to the circumcentre; this is an isosceles triangle, so dropping a perpendicular from the circumcentre to the side of the pentagon bisects the base of the triangle (side of the pentagon). From this the height of the triangle can be calculated using Pythagoras: half_side² + height² = radius² → (a cm)² + height² = (r cm)² →(2 cm)² + height² = (3.4 cm)² → height² = (3.4 cm)² - (2 cm)² → height = √(3.4² - 2²) cm area_pentagon = 5 × area_triangle = 5 × ½ × base × height = 5 × ½ × (2 × 2 cm) × √(3.4² - 2²) cm = 10 × √7.56 cm² = 27.495... cm² ≈ 27.5 cm² to 1 dp
What is the formula for measuring the area of a pentagon?
You didn't say it was a regular pentagon. For an arbitrary pentagon, you would calculate its area as you would for any polygon: divide it up into triangles, and add up the areas of the triangle. The area of a triangle is 1/2 times the base times the height, the height being the length of the perpendicular dropped to the base from the opposite vertex.
How do you find the surface area of pentagon-based pyramid with a slant height of 9?
There is not enough information to answer the question.
If the sides of a pentagon equals x what is the height?
1.78x
What is the area of an pentagon?
divide the pentagon into 5 equilateral triangles, and calculate their area. (base times height divided by 2) and when you have your answer, multiply it by 5.
Volume for a pentagon?
A pentagon is a two-dimensional geometric figure and therefore has area but not volume. To have volume, a geometric figure must have height or thickness as well as its plane dimensions.
What is the area of a regular pentagon if the radius r of the circumcircle is 3.4 cm and half the side length a is 2 cm rounded to 1 decimal place?
In a regular pentagon there are 5 vertices which connect to the circumcentre each a distance r = 3.4 cm away. This creates 5 triangles inside the pentagon; so the area of the pentagon is the sum of these five triangles; as the pentagon is regular, this is the same as 5 times the area of one of these triangles. The length of each side of the pentagon is twice half the length of one side → side = 2 × a = 2 × 2 cm Consider one side and the two radii connecting its ends to the circumcentre; this is an isosceles triangle, so dropping a perpendicular from the circumcentre to the side of the pentagon bisects the base of the triangle (side of the pentagon). From this the height of the triangle can be calculated using Pythagoras: half_side² + height² = radius² → (a cm)² + height² = (r cm)² →(2 cm)² + height² = (3.4 cm)² → height² = (3.4 cm)² - (2 cm)² → height = √(3.4² - 2²) cm area_pentagon = 5 × area_triangle = 5 × ½ × base × height = 5 × ½ × (2 × 2 cm) × √(3.4² - 2²) cm = 10 × √7.56 cm² = 27.495... cm² ≈ 27.5 cm² to 1 dp
How can i find the volume of pentagonal prism?
First you find the area of the base which is a pentagon. Then you multiply it by the height. So base times height equals volume.
What is the formula for measuring the area of a pentagon?
You didn't say it was a regular pentagon. For an arbitrary pentagon, you would calculate its area as you would for any polygon: divide it up into triangles, and add up the areas of the triangle. The area of a triangle is 1/2 times the base times the height, the height being the length of the perpendicular dropped to the base from the opposite vertex.
How do find the volume of a pentagon?
If you mean a pentagonal prism, then find the area of the pentagon 1st. Length of 1 side x 1.7, then multiply by the height of the prism. But I dont really know the regular Pentagon volume. sorry... hope you dont hate me for that.
How do you find the surface area of pentagon-based pyramid with a slant height of 9?
There is not enough information to answer the question.
What is the formula for finding area of a pentagon?
[ONLY WORKS FOR REGULAR PENTAGONS] I don't the exact formula, BUT, from what I learned in Geometry last year, I remember that if you have the radius from the center perpendicular to a side [for height] and if you have the length of the side of the pentagon, you can use a simple 1/2 times base time height to get 1/5th of the area. Then you just take that and multiply it by 5 to get the area of the whole pentagon. I know it looks complicated, but it's pretty simple: I have a REGULAR pentagon that I chop into 5 triangles I have the height = 2 I have the base [or the length of 1 side of the pentagon]= 4 1/2xbasexheight= 1/2x2x4= 4 So now you have the area of 1 triangle and multiply by 5 4x5= 20 your pentagon is 20 units squared. I hope this helped.
Formula of a perimeter?
The formula for finding out perimeters of shapes is length+length+height+height=perimeter or what else you can do is (lengthx2)+(heightx2)=PERIMETER
How do you calculate the volume of a pentagonal pyramid?
V = (1/3) (area of the base) (height) Area of a pentagon = 1/2 x apothem length x 5 x length of a side of the pentagonthe apothem is the perpendicular distance from the center of the pentagon to the side of the pentagon
What is the ratio of the height to the sides of a pentagon?
If the pentagon is a regular pentagon, then each of the central angles (formed by joinning the center with the vertices) is72⁰ (1/5 of 360⁰). So that 5 congruent isosceles triangle are formed, with base angles of 54⁰. If we draw the height, of these triangles (from the center to the sides of the pentagon), 10 congruent right triangles are formed. Let denote with: b the sides of the pentagon, and h the height. In one of the right triangles we have: tan 54⁰ = h/(b/2) tan 54⁰ = 2h/b 1.38 = 2h/b 2h = 1.38b h = (1.38/2)b h = .69b So that, h/b = .69b/b = .69
