Mathematics Question and Solution
a² = 11²+8²
a = √(121+64)
a = √(185) units.
a² = 4²+b²
√(185)² = 4²+b²
b² = 185-16
b = √(169)
b = 13 units.
b is the length of the 2 congruent rectangles.
c = b-11
c = 2 units.
Therefore, shaded area is;
Area trapezoid with parallel sides 8 units and 4 units, and height 13 units + Area trapezoid with parallel sides 13 units and 2 units, and height 8 units - Area triangle with height 4 units and base 13 units - Area triangle with height 8 units and base 11 units.
½(4+8)*13+½(2+13)*8-½(4*13)-½(11*8)
= (6*13)+(15*4)-(2*13)-(11*4)
= 78+60-26-44
= 138-70
= 68 square units.
