To find the area of the shaded section, we first need to calculate the area of the trapezium and then subtract the area of the triangle from it. Let's go through each step:

Step 1: Calculate the Area of the Trapezium

The formula for the area of a trapezium is: $\text{Area} = \frac{1}{2} \times (a + b) \times h$ where:

• $a = 25 \text{ cm}$ (the length of the top side),
• $b = 15 \text{ cm}$ (the length of the bottom side),
• $h = 14 \text{ cm}$ (the height).

$\text{Area of trapezium} = \frac{1}{2} \times (25 + 15) \times 14$ $= \frac{1}{2} \times 40 \times 14$ $= 20 \times 14 = 280 \text{ cm}^2$

Step 2: Calculate the Area of the Triangle

The formula for the area of a triangle is: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ where:

• The base of the triangle is $11 \text{ cm}$,
• The height of the triangle is $8 \text{ cm}$.

$\text{Area of triangle} = \frac{1}{2} \times 11 \times 8$ $= \frac{1}{2} \times 88$ $= 44 \text{ cm}^2$

Step 3: Subtract the Area of the Triangle from the Area of the Trapezium

$\text{Area of the shaded region} = \text{Area of trapezium} - \text{Area of triangle}$ $= 280 \text{ cm}^2 - 44 \text{ cm}^2$ $= 236 \text{ cm}^2$

Final Answer

The area of the shaded section is 236 cm².

Would you like more details or have any questions?

Relative Questions

1. What would happen to the shaded area if the dimensions of the triangle were doubled?
2. How would you calculate the area if the trapezium’s height was changed to 10 cm?
3. If the triangle was positioned differently within the trapezium, how would that affect the calculation?
4. What if the base lengths of the trapezium were equal, making it a rectangle? How would the area be calculated then?
5. How can you confirm the accuracy of the measurements if the figure states "Not drawn accurately"?

Tip

Always double-check the dimensions given in the problem, especially when figures are "not drawn accurately," to ensure calculations are based solely on the provided measurements.