Answer:
Area of rectangle PLUM = 75.00 square units
Step-by-step explanation:
Since diagonal of rectangle divides the rectangle into two equal triangles,
Therefore, area of the rectangle PLUM = 2× area of triangle PLM
By the mean proportional theorem,
In ΔPLM,
AP² = AM × AL
6² = AM × 8
AM = [tex]\frac{36}{8}[/tex]
AM = 4.5 units
Area of PLM = [tex]\frac{1}{2}(\text{Base})(\text{height})[/tex]
= [tex]\frac{1}{2}(ML)(AP)[/tex]
= [tex]\frac{1}{2}(8 + 4.5)(6)[/tex]
= 12.5 × 3
= 37.5 units²
Now area of rectangle PLUM = 2×37.5 = 75 units²
Therefore, area of the rectangle is 75.00 square units.
