The question asks to find the area of the two shaded figures (labeled A and B) on a grid where each square represents 1 square unit.

Figure A:

• This shape appears to be a right triangle.
• The base is 4 units long, and the height is 5 units.
• The area of a triangle is calculated by:

$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$

Substituting the values:

$\text{Area of A} = \frac{1}{2} \times 4 \times 5 = 10 \, \text{square units}$

Figure B:

• This shape resembles a combination of a triangle and a rectangle.
• The height of the entire shape is 5 units, and the width of the base is 5 units.
• To calculate the area, we break it into two parts:
  • Rectangle: With a base of 4 units and height of 3 units, its area is:

$\text{Area of rectangle} = 4 \times 3 = 12 \, \text{square units}$

• Triangle: The remaining part forms a triangle with a base of 2 units and a height of 2 units. The area is:

$\text{Area of triangle} = \frac{1}{2} \times 2 \times 2 = 2 \, \text{square units}$

Adding both areas together:

$\text{Total Area of B} = 12 + 2 = 14 \, \text{square units}$

Summary:

• Area of figure A = 10 square units
• Area of figure B = 14 square units

Would you like further details on these calculations or additional clarification?

Related Questions:

1. How do you calculate the area of irregular polygons?
2. What is the formula for the area of a right triangle?
3. How can breaking a shape into simpler shapes help in finding its area?
4. How can you use grid paper to estimate the area of irregular figures?
5. What are some strategies to verify the correctness of area calculations?

Tip: Always verify the measurements of base and height correctly from the grid before applying formulas for areas.