Answer:
[tex]area = area \: of \: trapezium + area \: of \: semi - circle \\ but \: height = \sqrt{ {15}^{2} - {(31 - 22)}^{2} } = 12 \: cm \\ area = \frac{1}{2} h(a + b) + \frac{1}{2} \pi {r}^{2} \\ = ( \frac{1}{2} \times 12 \times (22 + 31)) + ( \frac{1}{2} \times \frac{22}{7} \times ( \frac{12}{2} ) {}^{2} ) \\ = 318 + 56.57 \\ = 374.6 \: {cm}^{2} [/tex]
