The figure shows two similar trapeziums. CD=10cm(下底), AE=6cm(高), PQ=4cm(上底), RS=5cm(下底).
a) Find AB and the area of ABCD.
b) Find the area of PQRS.
Similar Trapeziums
2012-03-13 1:46 am
回答 (1)
2012-03-14 5:52 pm
✔ 最佳答案
Since ABCD and PQRS are similar trapeziumsThe ratios of their respective dimensions are constant
CD/RS = constant
CD = 10 cm, RS = 5 cm
10 cm/5 cm = 2
Size of dimension of smaller trapezium PQRS is half of the bigger trapezium ABCD
AB = PQ x 2 = 4cm x 2 = 8 cm
PT is height of trapeziums PQRS
PT = AE x 0.5 = 6 cm x 0.5 = 3 cm
(1) AB = 8 cm
Area ABCD = (top + bottom) x height/2
= (8 cm + 10 cm) x 6cm/2
= 54 sq. cm
(2) Area PQRS = (top + bottom) x height/2
= (4 cm + 5 cm)x 3 cm/2 = 13.5 sq. cm
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