Explanation:
we need to remember 2 things for right-angled triangles (which we need to use to find the sides of the rectangle, so that we then can calculate the area) :
1. Pythagoras
a² + b² = c²
with c being the Hypotenuse (the side opposite of the 90° angle), a and b being the legs.
2. geometric mean theorem
height = sqrt(p×q)
with p and q being the segments of the baseline the height is splitting it into. in our case MA and AL.
so, to get the length of the rectangle (PL) we use Pythagoras :
PL² = 6² + 8² = 36 + 64 = 100
PL = 10 units
to get PM we first need to get ML. and for that we need to get MA.
6 = sqrt(MA × 8)
36 = MA × 8
MA = 36/8 = 4.5 units
that means ML = 8 + 4.5 = 12.5 units
and again Pythagoras
ML² = PL² + PM²
12.5² = 10² + PM²
156.25 = 100 + PM²
56.25 = PM²
PM = 7.5 = 7.5 units
so, the area of the rectangle is
10 × 7.5 = 75 = 75.00 units²
to "round" to the nearest hundredth.