To find the area of the given shape, we can separate it into two simpler composite shapes: a rectangle and a right triangle.

Step 1: Identifying Composite Shapes

1. Rectangle: The bottom part of the figure is a rectangle.

   • Length (L) = 30 mm
   • Width (W) = 5 mm

2. Right Triangle: The top right part of the figure is a right triangle.

   • Base (b) = 20 mm (horizontal length)
   • Height (h) = 7 mm (vertical length)

Step 2: Calculating the Area of Each Shape

1. Area of the Rectangle: $A_{\text{rectangle}} = L \times W = 30 \, \text{mm} \times 5 \, \text{mm} = 150 \, \text{mm}^2$

2. Area of the Right Triangle: $A_{\text{triangle}} = \frac{1}{2} \times b \times h = \frac{1}{2} \times 20 \, \text{mm} \times 7 \, \text{mm} = \frac{1}{2} \times 140 \, \text{mm}^2 = 70 \, \text{mm}^2$

Step 3: Adding the Areas Together

The total area of the shape is the sum of the areas of the rectangle and the right triangle:

$A_{\text{total}} = A_{\text{rectangle}} + A_{\text{triangle}} = 150 \, \text{mm}^2 + 70 \, \text{mm}^2 = 220 \, \text{mm}^2$

Conclusion

The total area of the composite shape is 220 mm².

Would you like more details on any of these steps, or do you have any questions?

Related Questions

1. How do you calculate the perimeter of the composite shape?
2. What is the importance of separating composite shapes into simpler ones for calculations?
3. How would the area change if the dimensions of the shapes were doubled?
4. Can you explain how to calculate the area of a triangle given different parameters, like all three sides?
5. How can you determine the height of the triangle if only the area and base are given?

Tip

When dealing with composite shapes, breaking them down into simpler, known shapes (like rectangles and triangles) makes it easier to calculate areas and perimeters.