Area of Inscribed Equilateral Triangle of Circle | Can You Solve?

In this video, Brian Mclogan explains how to find the area of an equilateral triangle inscribed within a circle with a given radius. He begins by setting up the problem and encourages viewers to think about what they know. He then discusses the properties of equilateral triangles and special right triangles, specifically the 30-60-90 triangle. Using these properties, he calculates the area of the triangle step-by-step, demonstrating the process and simplifying the calculations. The video concludes with a summary of the solution and an invitation to subscribe for more content.

What is the first step in solving the problem of finding the area of an inscribed equilateral triangle?

• Determine the radius of the circle.

• Identify the properties of the triangle.

• Find the center of the circle.

• Calculate the circumference of the circle.

What is the measure of each angle in an equilateral triangle?

• 45 degrees

• 60 degrees

• 90 degrees

• 120 degrees

In a 30-60-90 triangle, if the shortest side is x, what is the length of the hypotenuse?

• x * sqrt(3)

• 2x

• x * sqrt(2)

• x

How do you find the height of an equilateral triangle using a 30-60-90 triangle?

• Divide the base by 2

• Multiply the shortest side by sqrt(3)

• Multiply the hypotenuse by 2

• Multiply the base by sqrt(3)/2

What is the formula for the area of a triangle?

• base * height

• 1/2 * base * height

• base - height

• base + height

How many smaller triangles are formed when an equilateral triangle is divided using its height?

• 3

• 6

• 2

• 4

What is the final step to find the total area of the inscribed equilateral triangle?

• Add the areas of all smaller triangles.

• Subtract the area of the circle from the triangle.

• Divide the area of one triangle by 6.

• Multiply the area of one triangle by 6.