To find the shaded area of the shape in the image, we can break it down into simpler geometric shapes and calculate the area for each.

Step 1: Analyze the Shape

The overall shape is a rectangle with a triangular section removed from the top middle.

• The outer rectangle has dimensions of 11 meters (width) by 9.9 meters (height).
• The triangular cutout is isosceles with a base of 8.5 meters and a height of 5.4 meters.

Step 2: Calculate the Area of the Rectangle

The area of the outer rectangle can be calculated using the formula for the area of a rectangle: $\text{Area of Rectangle} = \text{Width} \times \text{Height}$ $= 11 \, \text{m} \times 9.9 \, \text{m} = 108.9 \, \text{m}^2$

Step 3: Calculate the Area of the Triangular Cutout

The area of the triangle is calculated using the formula for the area of a triangle: $\text{Area of Triangle} = \frac{1}{2} \times \text{Base} \times \text{Height}$ $= \frac{1}{2} \times 8.5 \, \text{m} \times 5.4 \, \text{m} = 22.95 \, \text{m}^2$

Step 4: Calculate the Shaded Area

To get the shaded area, subtract the area of the triangular cutout from the area of the rectangle: $\text{Shaded Area} = \text{Area of Rectangle} - \text{Area of Triangle}$ $= 108.9 \, \text{m}^2 - 22.95 \, \text{m}^2 = 85.95 \, \text{m}^2$

Thus, the shaded area is 85.95 m².

Would you like further details or have any questions?

Here are some related questions for further practice:

1. How would the shaded area change if the triangle's height were increased?
2. What would be the shaded area if the base of the triangle were 10 meters instead of 8.5 meters?
3. How do you calculate the perimeter of the entire shaded shape?
4. What is the effect on the shaded area if the entire rectangle's width decreases by 1 meter?
5. How can you verify the calculations using different methods or tools?

Tip: When breaking down composite shapes, identify basic geometric figures like rectangles and triangles for easier calculations.