$$A=\frac{a·h_a}{2}=\frac{b·h_b}{2}$$

$$\frac{a·20}{2}=\frac{b·24}{2}$$

$$10·a=12·b$$

$$\frac{10·a}{12}=b$$

$$\frac{\bcancel{2}·5·a}{\bcancel{2}·6}=b$$

$$b=\frac{5·a}{6}$$

The height h_a divides the isosceles triangle into two equal (congruent) right triangles. Write the Pythagorean theorem for these triangles.

$$b^2={\left(\frac{a}{2}\right)}^2+h_a^2$$

$$b^2=\frac{a^2}{4}+h_a^2 |·4$$

$$4·b^2=a^2+4·h_a^2$$

$$4·{\left(\frac{5}{6}a\right)}^2=a^2+4·{20}^2$$

$$4·\frac{25}{36}{a}^2=a^2+4·400$$

$$\bcancel{4}·\frac{25}{\bcancel{4}·9}{a}^2=a^2+4·400$$

$$\frac{25}{9}{a}^2=a^2+1600|·9$$

$$25a^2=9a^2+14400$$

$$25a^2-9a^2=14400$$

$$16a^2=14400$$

$$a^2=\frac{14400}{16}$$

$$a^2=900$$

$$a=\sqrt{900}$$

$$a=30$$

$$A=\frac{a·h_a}{2}$$

$$A=\frac{30·20}{2}=\frac{30·10·\bcancel{2}}{\bcancel{2}}$$

$$A=300 c{m}^2$$