Answer:
a. 3 cm
b. 72 cm²
Step-by-step explanation:
1a. The area of a trapezium is the average of the parallel sides times the height.
A = ½ (b₁ + b₂) h
21 = ½ (5 + 9) h
h = 3 cm
1b. PQTU is a parallelogram, so UT = 4 cm. Also, PQRS is a parallelogram, so RS = 4 cm. Therefore, RU = 4 + 4 + 6 = 14 cm.
Next, the area of a parallelogram is the base times the perpendicular height.
A = bh
32 = 4h
h = 8 cm
Therefore, the area of the trapezium is:
A = ½ (b₁ + b₂) h
A = ½ (4 + 14) (8)
A = 72 cm²
