if you join all the vertices of a heptagon how many quadrilaterals will you get?
Wow that answer is so wrong. There are 7 vertices, and each quadrilateral does have 4. That much is true. But this problem requires a bit deeper thinking. You need to determine how many quads. each vertex will create. The answer is 5. Multiply that number by the # of vertices (7), and you will get the ACTUAL answer...35. You can do this by drawing it out for one vertex and then multiplying by 7.
To find the number of quadrilaterals that can be formed by joining the vertices of a heptagon, you can use the combination formula.
A heptagon has 7 vertices. To form a quadrilateral, you need to select 4 points out of these 7 vertices, as the order of the points doesn't matter.
Using the combination formula, the number of ways to choose 4 points out of 7 is given by:
C(n, r) = n! / (r! * (n - r)!)
where n is the total number of items, and r is the number of items you want to choose.
Plugging in the values, we have:
C(7, 4) = 7! / (4! * (7 - 4)!)
Simplifying:
C(7, 4) = 7! / (4! * 3!)
C(7, 4) = (7 * 6 * 5 * 4!) / (4! * 3!)
C(7, 4) = (7 * 6 * 5) / 3!
C(7, 4) = (7 * 6 * 5) / (3 * 2 * 1)
C(7, 4) = 7 * 5
C(7, 4) = 35
Therefore, there are 35 quadrilaterals that can be formed by joining the vertices of a heptagon.
To determine the number of quadrilaterals you can form by joining the vertices of a heptagon, we need to understand the properties of a quadrilateral and the heptagon.
A quadrilateral is a polygon with four sides and four vertices. We want to form a quadrilateral by joining the vertices of a heptagon, which is a polygon with seven sides and seven vertices.
To create a quadrilateral, we need to select 4 out of the 7 vertices of the heptagon, as any four non-collinear points determine a unique quadrilateral.
To find the number of ways to choose 4 vertices from a set of 7, we can use the concept of combinations.
The number of combinations of n objects taken r at a time can be calculated using the formula:
C(n,r) = n! / (r!(n-r)!)
In this case, n = 7 (the number of vertices) and r = 4 (the number of vertices required to form a quadrilateral).
Using the formula, we can calculate it as follows:
C(7,4) = 7! / (4!(7-4)!).
= (7 * 6 * 5 * 4!) / (4!(3!)).
= (7 * 6 * 5) / (3 * 2 * 1).
= 35.
Therefore, by joining all the vertices of a heptagon, you can form a total of 35 quadrilaterals.
A Heptagon has 7 sides, and, therefore,
7 vertices. There are 4 vertices per Quadralateral.
7/4 = 1 3/4 Quadralateral.