A triangular flower bed in a park has sides measuring 20 m, 20 m and 24 m. What is its area in square metres?

Only the three sides are given, so use Heron'$s$ formula: $s=(20+20+24)/2=32$ and area = √$(32\times 12\times 12\times 8)$ = √36864 = 192 sq m. The base-and-height route agrees: dropping a perpendicular onto the 24 m base splits it into 12 m halves, so the height is √$(20^2-12^2)=16$ m and the area is $(1/2)\times 24\times 16=192$. The trap 240 is $(1/2)\times 20\times 24$, which pairs the base with a SIDE instead of with the perpendicular height; 384 is $24\times 16$ with the 1/2 forgotten; 96 halves the correct answer a second time.