I WILL GIVE BRAINLY! The surface of a table to be built will be in the shape shown below. The distance from the center of the sh
ape to the center of each side is 8.7 inches and the length of each side is 10 inches. A hexagon labeled ABCDEF is shown will all 6 sides equal in length. ED is labeled as 10 inches. A perpendicular is drawn from the center of the hexagon to the side ED. This perpendicular is labeled as 8.7 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)
2 answers:
Answer:
- draw lines center to vertex
- 43.5 square inches
- 261 square inches
Step-by-step explanation:
<u>Part A</u>:
The area can be decomposed into triangles by drawing a line from the center to each vertex of the hexagon.
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<u>Part B</u>:
The area of each triangle is given by the triangle area formula:
A = (1/2)bh
A = (1/2)(10 in)(8.7 in) = 43.5 in²
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<u>Part C</u>:
The area of the table top is 6 times the area of one triangle:
surface area = 6(43.5 in²) = 261 in²
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