Question

The surface of a table to be built will be in the shape shown below. The distance from the center of the shape to the center of each side is 7.8 inches and the length of each side is 9 inches.

A hexagon labeled ABCDEF is shown will all 6 sides equal in length. ED is labeled as 9 inches. A perpendicular is drawn from the center of the hexagon to the side ED. This perpendicular is labeled as 7.8 inches.

Part A: Describe how you can decompose this shape into triangles. (2 points)

Part B: What would be the area of each triangle? (5 points)

Part C: Using your answers above, determine the area of the table's surface. (3 points)

Answer 1

Answer:

I can only answer part B because that all i know sorry but i think its 6

Step-by-step explanation:

Answer 2

Concept Introduction:

Hexagon have six edges and six vertices. Hence it can be divided into triangles by connecting the vertices of hexagon to center of the hexagon. One hexagon have six triangles.

Given: The surface of a table to be built will be in the shape shown below. The distance from the center of the shape to the center of each side is $7.8 inches$ and the length of each side is $9 inches$.

To Find:

We have to find the value of, area of triangle and the hexagon.

Solution:

According to the problem,

A)Hexagon have six edges and six vertices. Hence it can be divided into triangles by connecting the vertices of hexagon to center of the hexagon. One hexagon have six triangles.

B) Area of triangle = 1/2*height*base=$1/2*7.8*9=35.1inch^{2}$

C) Area of hexagon = $6*area of triangle = 35.1*6=210.6inch^{2}$

Final Answer:

The value of Area of triangle = $35.1inch^{2}$

Area of hexagon = $210.6inch^{2}$.

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