To find the area of the regular hexagon, we need to divide it into 6 equilateral triangles and find the area of one of those triangles.
Since we are given side lengths a = 7 inches and b = 10 inches, we know that the height of the triangle (which is also the apothem of the hexagon) can be found using the formula:
h = sqrt(b^2 - (a/2)^2)
= sqrt(10^2 - (7/2)^2)
= sqrt(100 - 12.25)
= sqrt(87.75)
≈ 9.36 inches
Now, the area of one of the triangles can be calculated as:
Area of one triangle = (1/2) * base * height
= (1/2) * a * h
= (1/2) * 7 * 9.36
= 33.18 in2
Since there are 6 equilateral triangles in a regular hexagon, the total area of the regular hexagon is:
Area of hexagon = 6 * Area of one triangle
= 6 * 33.18
= 199.08 in2
Thus, the closest option is not listed, but the closest value provided is Option C: 210 in2.
Find the area of the regular hexagon below by using the area formula for triangles.
a = 7 inches and b = 10 inches
*picture not drawn to scale
A.
30 in2
B.
70 in2
C.
210 in2
D.
35 in2
1 answer
2 answers