A field is divided into eight sections as shown below - Leaving Cert Mathematics - Question 5 - 2017

To find the height $x$, we can use the area equation derived from the trapezoidal rule. Given:

$145-6 = \frac{1}{2} \times 4 \times (6.4 + 6.9 + 6 + 6 + x + 2)$

We can simplify the equation:

• First calculate the sum of heights:
• Total heights evaluated = 6.4 + 6.9 + 6 + 6 + 2 = 27.3
• Plugging this into the formula results in:

$139 = \frac{1}{2} \times 4 \times (27.3 + x)$

This simplifies to:

$139 = 2(27.3 + x)$

Expanding this yields:

$139 = 54.6 + 2x$

Isolating $x$:

$2x = 139 - 54.6 = 84.4$ $x = \frac{84.4}{2} = 42.2$

Thus, the value of the height marked $x$ is approximately 42.2 m.