Question

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a carpenter makes a table in the shape of a regular octagon. what is the area of the table?
the octagon can be divided into 8 imaginary triangles each with an area of approximately ▼ square feet. the total area of all 8 triangles is approximately ▼ square feet.
(image of a regular octagon with a right triangle inside, showing a leg of 3 ft and a height of 3.621 ft)

Explanation:

Step1: Calculate area of 1 triangle

Area of a triangle: $\frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 3 \times 3.621$
$\frac{1}{2} \times 3 \times 3.621 = 5.4315$

Step2: Calculate total area of octagon

Multiply 1 triangle area by 8: $5.4315 \times 8$
$5.4315 \times 8 = 43.452$

Answer:

The area of one triangle is approximately 5.43 square feet. The total area of the table is approximately 43.45 square feet.