Spiral Revievi (6.G.1, 6.G.2, 6.G.4)
3. A regular decagon has side lengths of
4 centimeters long. If the decagon is divided
into 10 congruent triangles, each has an
approximate height of 6.2 centimeters.
What is the approximate area of the decagon?

Question

UpStudy AI · Accepted Answer

To find the approximate area of the regular decagon, we can use the formula for the area of a polygon divided into triangles. The area $$ A $$ of the decagon can be calculated using the formula:

$$
A = \text{Number of triangles} \times \text{Area of one triangle}
$$

1. **Number of triangles**: Since the decagon is divided into 10 congruent triangles, we have:
   $$
   n = 10
   $$

2. **Area of one triangle**: The area $$ A_t $$ of one triangle can be calculated using the formula:
   $$
   A_t = \frac{1}{2} \times \text{base} \times \text{height}
   $$
   Here, the base of each triangle is the side length of the decagon, which is 4 cm, and the height is approximately 6.2 cm.

Now, let's calculate the area of one triangle and then the total area of the decagon.

First, we calculate the area of one triangle:

$$
A_t = \frac{1}{2} \times 4 \times 6.2
$$

Next, we will multiply the area of one triangle by the number of triangles to find the total area of the decagon:

$$
A = n \times A_t
$$

Let's perform these calculations step by step.

First, calculate $$ A_t $$:
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{1}{2}\times 4\times 6.2$$
- step1: Multiply the terms:
  $$2\times 6.2$$
- step2: Multiply the numbers:
  $$12.4$$
The area of one triangle $$ A_t $$ is approximately $$ 12.4 $$ square centimeters.

Now, we can calculate the total area of the decagon $$ A $$ by multiplying the area of one triangle by the number of triangles:

$$
A = 10 \times 12.4
$$

Let's calculate this:
Calculate the value by following steps:
- step0: Calculate:
  $$10\times 12.4$$
- step1: Multiply the numbers:
  $$124$$
The total area of the decagon $$ A $$ is approximately $$ 124 $$ square centimeters.

Thus, the approximate area of the decagon is $$ 124 \, \text{cm}^2 $$.
The approximate area of the decagon is 124 square centimeters.

Spiral Revievi (6.G.1, 6.G.2, 6.G.4)
3. A regular decagon has side lengths of
4 centimeters long. If the decagon is divided
into 10 congruent triangles, each has an
approximate height of 6.2 centimeters.
What is the approximate area of the decagon?

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Spiral Revievi (6.G.1, 6.G.2, 6.G.4) 3. A regular decagon has side lengths of 4 centimeters long. If the decagon is divided into 10 congruent triangles, each has an approximate height of 6.2 centimeters. What is the approximate area of the decagon?

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Answer

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Latest Geometry Questions

Spiral Revievi (6.G.1, 6.G.2, 6.G.4)
3. A regular decagon has side lengths of
4 centimeters long. If the decagon is divided
into 10 congruent triangles, each has an
approximate height of 6.2 centimeters.
What is the approximate area of the decagon?