Answer:
144 cm²
Explanation:
5x + 12x + 6x + 5x = 56
=> 28x = 56
=> x = 2
DC => 6x = 6(2) = 12
AB => 12x = 12(2) = 24
BC => 5x = 5(2) = 10
AD => 5x = 5(2) = 10
trapezium is an isosceles trapezium because a trapezium with a pair of non-parallel sides(BC&AD) that have equal distances, which are congruent, is an isosceles trapezium.
Thus, the base of the two triangles on each side are congruent.
base: (AB - DC) ÷ 2 = (24 - 12) ÷ 2 = 6
calculate the height using Pythagorean theorem => √10² - 6² = 8
area of the isosceles trapezium ABCD: (12 + 24) × 8 ÷ 2 = 144