Question 1: Calculate the length of each side of an equilateral triangle if its height measures 6 cm.

Answer: 6√3 cm

Question 2: Find the area of an equilateral triangle with side length 10 meters.

Answer: 25√3 m²

Question 3: Construct an equilateral triangle with sides of 8 cm on the grid. Show all your steps.

Answer: Students will draw and label the triangle correctly.

Question 4: Determine the height of an equilateral triangle with side length 12 inches.

Answer: 6√3 inches

Question 5: A garden is designed in the shape of an equilateral triangle with each side measuring 15 meters. Calculate the total length of fencing needed.

Answer: 45 meters

Question 6: What is the measure of each interior angle of an equilateral triangle? Explain your reasoning.

Answer: 60°; because the sum of angles in a triangle is 180°, and all angles are equal in equilateral triangles.

Question 7: If the side length of an equilateral triangle increases by 50%, how does its area change?

Answer: The area increases by 125%, since area is proportional to the square of the side length.

Question 8: Calculate the perimeter of an equilateral triangle whose side length is 9√2 cm.

Answer: 27√2 cm

Question 9: A flagpole is topped with a small decorative element in the shape of an equilateral triangle with side length 3 inches. Find the height of this triangle.

Answer: 3√3/2 inches

Question 10: Identify and correct the mistake: 'In an equilateral triangle, all sides are equal, and all angles are 90°.'

Answer: All angles measure 60°, not 90°.

Question 11: Find the side length of an equilateral triangle if its area is 16√3 cm².

Answer: 8 cm