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
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.