Question 1: Shade exactly half of the rectangle on the grid and calculate the area of the shaded region if the rectangle measures 8 cm by 6 cm.

Answer: 24 cm^2

Question 2: A circle with radius 4 cm is drawn inside a square of side 10 cm. Shade the semicircular region on the right half of the circle. Calculate the area of the shaded region.

Answer: 32π cm^2

Question 3: On the grid, shade 3 equal parts of a triangle divided into 9 smaller congruent triangles. Calculate the area of the shaded region if the large triangle has an area of 18 cm^2.

Answer: 6 cm^2

Question 4: Construct and shade a parallelogram within the grid so that it has an area of 12 cm^2, using only the grid lines. Explain your construction steps.

Answer: Student’s explanation of drawing parallel lines and counting squares to ensure the area equals 12 cm^2.

Question 5: A square is divided into 16 smaller equal squares. Shade 3/4 of the entire square. How many small squares are shaded? Show your working.

Answer: 12

Question 6: Identify and correct the mistake: A student shades 2/3 of a rectangle measuring 9 cm by 6 cm but claims that the shaded area is 12 cm^2. What is the correct shaded area?

Answer: 18 cm^2

Question 7: Plot the graph of y = 2x for x values from 0 to 5. Shade the region between the line and the x-axis. What is the area of the shaded region?

Answer: 25 units^2

Question 8: A rectangular garden measuring 15 m by 10 m needs to be partially shaded to create a walking path of 2 m width around the border. Shade the remaining area of the garden. Calculate the shaded area's size.

Answer: 175 m^2

Question 9: A complex shape is divided into 4 regions, each with different shading patterns. If the total area is 24 cm^2, and the shaded regions are 1/4, 1/3, 1/6, and the remaining unshaded, find the areas of all shaded regions.

Answer: Shaded regions: 6 cm^2, 8 cm^2, 4 cm^2; Unshaded: 6 cm^2

Question 10: A pentagon shape on the grid is divided into 5 equal triangular sectors. Shade 2 sectors. Calculate the total area of the pentagon if each sector has an area of 3 cm^2.

Answer: 6 cm^2

Question 11: Explain how shading can be used to visually represent fractions within shapes. Provide a brief example based on a rectangle divided into 10 parts, with 7 shaded.

Answer: Shading 7 out of 10 parts visually shows the fraction 7/10, helping to understand parts of a whole.