Triangle Properties and Area Calculations

The video tutorial explains how to find the area of a shaded region between two equilateral triangles. It begins by introducing the problem and then derives the formula for the area of an equilateral triangle using the properties of 30-60-90 triangles. The tutorial then applies this formula to calculate the areas of the larger and smaller triangles, subtracting the latter from the former to find the shaded area. The final result is approximated using a calculator.

What is the length of each side of the larger equilateral triangle?

• 12

• 10

• 16

• 14

What is the formula for the area of a triangle?

• 1/2 base times height

• base times height

• 1/3 base times height

• base plus height

What is the angle measure in an equilateral triangle?

• 120 degrees

• 90 degrees

• 60 degrees

• 45 degrees

What is the ratio of the sides in a 30-60-90 triangle?

• 1:1:1

• 1:2:3

• 1:√2:2

• 1:√3:2

How do you calculate the height of an equilateral triangle with side length s?

• s

• s√3/2

• s/2

• s√2/2

What is the area of the larger triangle using the derived formula?

• √3/4 times 4 squared

• √3/2 times 4 squared

• √3/2 times 14 squared

• √3/4 times 14 squared

What is the area of the smaller triangle using the derived formula?

• √3/4 times 14 squared

• √3/2 times 14 squared

• √3/4 times 4 squared

• √3/2 times 4 squared

What is the difference between the areas of the larger and smaller triangles?

• 180

• 196

• 16

• 45

What is the final calculated area of the shaded region in terms of square roots?

• 196√3

• 77.94

• 45√3

• 16√3

What is the approximate decimal value of the shaded area?

• 45.00

• 16.00

• 77.94

• 196.00