Let's analyze the uploaded image.

The task is to find the area of each figure. The grid squares are 1 unit by 1 unit, and there are various shapes provided (a triangle, rectangle, and circle). I'll now calculate the areas of the figures visible in the image.

Figure 18 (Triangle)

Formula for the area of a triangle: $A = \frac{1}{2} \times b \times h$

• Base $b = 10 \, \text{ft}$
• Height $h = 4 \, \text{ft}$

$A = \frac{1}{2} \times 10 \times 4 = 20 \, \text{ft}^2$

Figure 19 (Rectangle)

Formula for the area of a rectangle: $A = l \times w$

• Length $l = 8 \, \text{units}$
• Width $w = 4 \, \text{units}$

$A = 8 \times 4 = 32 \, \text{square units}$

Figure 20 (Circle)

Formula for the area of a circle: $A = \pi r^2$

• Radius $r = 3 \, \text{dm}$

$A = \pi (3)^2 = \pi \times 9 \approx 28.27 \, \text{dm}^2$

Figure 22 (Triangle on a Grid)

The triangle's area can also be found using: $A = \frac{1}{2} \times b \times h$ From the grid:

• Base $b = 8 \, \text{units}$
• Height $h = 6 \, \text{units}$

$A = \frac{1}{2} \times 8 \times 6 = 24 \, \text{square units}$

Summary of Areas

1. Figure 18 (Triangle): $20 \, \text{ft}^2$
2. Figure 19 (Rectangle): $32 \, \text{square units}$
3. Figure 20 (Circle): $\approx 28.27 \, \text{dm}^2$
4. Figure 22 (Triangle): $24 \, \text{square units}$

Would you like me to explain any of these calculations further or provide details on rounding or formulas?

Follow-Up Questions:

1. What is the significance of understanding the relationship between base and height in area calculations for triangles?
2. How is the area of a circle affected when the radius is doubled?
3. Can you derive the area formulas for other shapes, like parallelograms or trapezoids?
4. What is the difference between square units and square feet, and how do you convert between them?
5. How can grid-based figures help in estimating irregular areas?

Tip:

Always label your measurements (e.g., feet, meters, units) to avoid confusion and ensure accuracy when working with formulas!