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Triangle: The other shapes have an even number of sides.
Square: The numbers of sides on the other two is divisible by 3
Hexagon: For sides of a fixed length, the other two shapes are rigid structures (the square can distort to a rhombus but then it is no longer a square.)
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Triangle: It can have all acute angles.
Square: It can (must ) have all right angles.
Hexagon: It can have all obtuse angles.
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What is the area of a regular hexagon with a side of 4 and an apothem of 3 46?
Easy. Since the side is the base and the apothem is the height of the triangle, multiply them and divide by two to get the area of the triangle. 3 * 3.46 = 10.38 /2 = 5.19. Then multiply by 6 to get the area of the hexagon. 5.19 * 6 = 31.14. You multiply by 6 because you can fit 6 regular triangles in a regular hexagon. We've already found the area of one regular triangle in the hexagon.
How can you find the generalization for square pentagon and hexagon?
They all have at least one pair of parallel lines
What is a triangle with an area of 12 square units?
It's half the size of a quadrilateral with 24 square units ------------ One type of triangle with an area of 12 square units is the isosceles triangle with two 5-unit sides and one 6-unit side.
What is the area of a regular hexagon if a side is 30?
The area is about 2338.27 square units, from the formulaA = 3/2 (sqrt 3) s2 or about 2.598 s2--Let's draw a segment from the center of the hexagon to the middle of a side. This segment is called the apothem. Then use the 30-60-90 triangle rule. If half of a side is 15, that means the apothem is 15√3.If we divide the hexagon into equilateral triangles, we get 6 equilateral triangles.So if we find the area for one of these triangles and multiply it by 6, we get the area of the hexagon. The area of a triangle is found by 1/2(b*h). The apothem is your height for the triangles. So plug the numbers in: 1/2(30*15√3). Solve: 1/2(779.4228) = 389.7114. This is the area of one triangle. Now we multiply by 6, and this becomes: 2338.2686
Can a right triangle have all side that are an odd number?
No. Here's why: you have a² + b² = c². If a is odd, then a² will also be odd (and if a is even, then a² will also be even. Same goes true for b² and c².If a² & b² are both odd, then you have odd + odd, which is even. Why is {odd + odd} always even, you may ask. An informal proof could be something like this:Let m & n be non-zero integers.So 2m and 2n are guaranteed to be even,then (2m + 1) & (2n + 1) are both odd.Add them together: (2m + 1) + (2n + 1) = 2m + 2n + 2 = 2(m + n + 1) which is even.And why is a² odd, when a is odd: if a is odd, then it does not have 2 as one of its factors. Since you square the number, you have not added any additional factors, so it still does not have 2 as a factor. If a was even, then it will have 2 as a factor, when you square it, you now have 2 as well as 2² as a factor, so the square is even as well.
