Question 1: Calculate the area of the shaded region in a rectangle measuring 12 cm by 8 cm, where 1/4 of the rectangle is shaded.

Answer: 24 cm²

Question 2: On a circular disc with radius 10 cm, a sector of 60° is shaded. Calculate the area of the shaded sector.

Answer: 52.36 cm² (approximate)

Question 3: Construct a triangle on the grid that has a base of 6 units and a height of 4 units. Shade the region representing the triangle.

Answer: Student draws and shades the triangle accordingly.

Question 4: A trapezoid with bases measuring 8 cm and 5 cm, and height 6 cm, is shaded in a diagram. Calculate the shaded area.

Answer: 39 cm²

Question 5: A rectangular engineering component measures 20 cm by 15 cm. If 1/3 of the surface is to be painted and shaded for insulation, what area will be shaded?

Answer: 100 cm²

Question 6: A gear with a diameter of 14 cm has a shaded sector of 90°. Calculate the area of the shaded sector.

Answer: 54.98 cm² (approximate)

Question 7: In an engineering drawing, a shaded region represents the material to be removed for a slot. If the slot is a rectangle measuring 4 cm by 2 cm, how much area is shaded?

Answer: 8 cm²

Question 8: A circular pipe with radius 5 cm has a segment shaded, representing a partial cut. The segment subtends a 120° angle at the center. Calculate the shaded area.

Answer: 10.47 cm² (approximate)

Question 9: A rectangular frame measures 30 cm by 20 cm, with a central rectangular opening measuring 10 cm by 5 cm. Shade the remaining region and calculate its area.

Answer: 550 cm²

Question 10: Identify and correct the mistake in shading a triangle where the height is mistakenly taken as 6 units instead of 4 units. Explain your correction.

Answer: Incorrect area; correct height is 4 units, so area = ½ × base × height, with the corrected height.

Question 11: A complex engineering component involves shading multiple regions. Describe a step-by-step method to accurately shade a combined region consisting of a rectangle and a semicircle. No drawing required.

Answer: Method involves calculating individual areas first, then shading the combined region, ensuring no overlaps or gaps.

Question 12: A challenging problem: On a grid, construct a pentagon with sides of 5 units each, and shade the region. Calculate the total area of the shaded pentagon.

Answer: Approximately 43.64 units² (using regular pentagon area formula).