Mensuration Practice Test 3

Right-angled isosceles triangle
By Pythagoras theorm,
${\left(\mathit{B}\mathit{C}\right)}^2$ = ${\left(\mathit{A}\mathit{C}\right)}^2+{\left(\mathit{A}\mathit{B}\right)}^2$
${\mathit{a}}^2$ = ${\mathit{x}}^2+{\mathit{x}}^2$
${\mathit{a}}^2$ = $2{\mathit{x}}^2$
= $\sqrt{\frac{{\mathit{a}}^2}{2}}$ = x

Area of the triangle = $\frac{1}{2}$ × base × height
= $\frac{1}{2}\times \sqrt{\frac{{\mathit{a}}^2}{2}}\times \sqrt{\frac{{\mathit{a}}^2}{2}}$
= $\frac{{\mathit{a}}^2}{4}\mathit{c}{\mathit{m}}^2$
Volume of the prism = Base × height
= $\frac{{\mathit{a}}^2}{4}\times \mathit{h}$ = $\frac{{\mathit{a}}^2\mathit{h}}{4}\mathit{c}{\mathit{m}}^3$