$\left(0\,0\right)\,\left(-5\,h\right)\,\left(20\,h\right)\,\left(15\,0\right)$ 

$y_L\=-2\sqrt{2} x$ and $y_R\=2\sqrt{2}\left(x-15\right)$

$A\=\frac{\left(15\+25\right)}{2} \left(10\sqrt{2}\right)\=200\sqrt{2}$ 

Initialize

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Define $h\,P\,Q\,R\,S$

$h\=10\sqrt{2}$$\stackrel{\text{assign}}{\to }$

$P\=\left[0\,0\right]$$\stackrel{\text{assign}}{\to }$

$Q\=\left[-5\,h\right]$$\stackrel{\text{assign}}{\to }$

$R\=\left[20\,h\right]$$\stackrel{\text{assign}}{\to }$

$S\=\left[15\,0\right]$$\stackrel{\text{assign}}{\to }$

Area of the trapezoid

$A\=\frac{15\+25}{2}h$$\stackrel{\text{assign}}{\to }$

Equations of the left and right edges

$$\begin{gathered} \mathrm{Line}\left(P\,Q\right)\left[1\right]\; \\ \mathrm{Line}\left(R\,S\right)\left[1\right] \end{gathered}$$

$y\=-2\sqrt{2}x$

$y_L\=-2\sqrt{2}x$$\stackrel{\text{assign}}{\to }$

$y_R\=2\sqrt{2}\left(x-15\right)$$\stackrel{\text{assign}}{\to }$

Apply the formula $\stackrel{\&conjugate0;}{y}\=\frac{1}{A}{\int }_a^b\left(f^2\left(x\right)-g^2\left(x\right)\right)\/2 \mathit{\ⅆ}x$ from Table 5.7.1

$\frac{1}{2 A}\left({\int }_{-5}^0\left(h^2-y_L^2\right) \mathit{\ⅆ}x\+{\int }_0^{15}{h}^2 \mathit{\ⅆ}x\+{\int }_{15}^{20}\left(h^2-y_R^2\right) \mathit{\ⅆ}x\right)$ = $\frac{65}{12}\sqrt{2}$$\stackrel{\text{at 10 digits}}{\to }$$7.660323461$$$