Given,
The base is
[tex]B\text{ = 10 in.}[/tex]
The height is
[tex]H=8.7\text{ in.}[/tex]
To find: Area of each triangle and the area of the table surface.
Solution:
Draw a line from each vertex to the vertex on the opposite side of the hexagon, you will form 6 triangles.
The area of each triangle is calculated by the formula.
[tex]Area\text{ of each triangle = }\frac{1}{2}\times B\times H[/tex]
Put the given values in the formula.
[tex]\begin{gathered} Area\text{ of each triangle = }\frac{1}{2}\times10\text{ in. }\times8.7\text{ in.} \\ Area\text{ of each triangle = 43.5 in.}^2 \end{gathered}[/tex]
Thus, the area of each triangle is 43.5 in.^2
Now, the area of the table surface is
[tex]43.5\times6=261\text{ in.}^2[/tex]
Thus, the area of the table surface is 261 in.^2.
