Sign In
To determine the area of this shape, we can divide the hexagon into 6 congruent isosceles triangles by drawing segments from the hexagon's vertices to its center.
To calculate the area of the hexagon we should find the area of one triangle and then multiply that result by 6. We need to know the triangle's height and base. We already know that the base is 1 yard. To find the height, we will use the fact that the corresponding height bisects the top angle, which must be 360^(∘)6=60^(∘) since it is a regular hexagon.
Notice that the height divides the triangle into two 30^(∘)-60^(∘)-90^(∘) triangles. In such a triangle, the longer leg is always sqrt(3) times greater than the shorter leg. With this information we can determine the height of the triangle as 12sqrt(3) yards.
b= 1/2sqrt(3), h= 1
Commutative Property of Multiplication
Multiply fractions
Identity Property of Multiplication
1/b* a = a/b
a*b/c= a* b/c
Cross out common factors
Simplify quotient
a/1=a
Multiply
