Question 1: Calculate the area of a triangle with sides a=8 cm, b=6 cm, and included angle C=60°. Use the formula ½abSinC.

Answer: 20.78

Question 2: A triangle has sides a=10 m, b=7 m, and angle C=45°. Find the area using the formula ½abSinC.

Answer: 24.64

Question 3: If two sides of a triangle are 9 cm and 12 cm, and the included angle is 30°, what is the area?

Answer: 27.0

Question 4: A common mistake is to forget to convert the angle to radians when using a calculator. Identify and correct the error in calculating the area with sides 7 cm, 9 cm, and angle 90°.

Answer: Ensure angle is in degrees or that calculator is set to degrees; area = ½×7×9×sin(90°)=31.5

Question 5: Construct a triangle on the grid with sides of 5 cm and 7 cm, and an included angle of 120°. Calculate its area.

Answer: 13.66

Question 6: A triangle has sides a=6 m, b=8 m, and the included angle C=75°. Calculate the area, then explain why using ½ab simply as base×height might be incorrect in this case.

Answer: Area = ½×6×8×sin75° ≈ 27.58; because the triangle is not right-angled, base×height only works if the height is known and perpendicular.

Question 7: Given a triangle with sides 10 cm, 14 cm, and an included angle of 50°, verify your area calculation using the formula and discuss any common errors.

Answer: Area ≈ ½×10×14×sin50° ≈ 106.7; error occurs if angle is not in radians or if sine value is incorrect.

Question 8: Plot a triangle with sides 7 cm, 9 cm, and an included angle of 60° on the grid. Estimate its area.

Answer: Approximately 54.9

Question 9: A student calculates the area of a triangle with sides 5 cm and 5 cm and an included angle of 180°. Identify the mistake and correct it.

Answer: Incorrect because angle 180° makes the triangle degenerate; area = 0.

Question 10: Using the formula ½abSinC, compute the area of a triangle with sides 11 cm and 13 cm, and angle C=95°. Is this a valid calculation? Why or why not?

Answer: Yes, it is valid; area ≈ ½×11×13×sin95° ≈ 70.5; the formula applies to any non-right-angled triangle.

Question 11: What common misconception might lead students to mistakenly use the formula for right-angled triangles in non-right-angled cases? Explain briefly.

Answer: They may assume the base and height are perpendicular without checking the angle; proper use requires the included angle between sides.