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2 years ago

Trapezia ABCD and PQRS are similar. Find the area shaded in green.

Mathematics

1 answer:

avanturin [10]2 years ago

6 0

The area shaded in green is 864 cm²

<h3>Similar figures</h3>

Similar figures, corresponding angles are congruent and the sides are ratio of each other. Therefore,

AB / PQ = CD / RS

30 / 10 = 24 / RS

30RS = 240

RS = 240 / 30

RS = 8 cm

let find the height of trapezium PQRS.

AB / PQ = 36 / h

30 / 10 = 36 / h

30h = 360

h = 360 / 30

h = 12 cm

Therefore,

area of the green portion = area of ABCD - area of PQRS

<h3>Area of a trapezium</h3>

area = 1 / 2(a + b)h

Therefore,

area of ABCD = 1 / 2(24 + 30)36 = 1 / 2 (54)36 = 1944 / 2 = 972 cm²

area of PQRS = 1 / 2(10 + 8)12 = 1 / 2(18)12 = 216 / 2 = 108 cm²

Area of the green portion = 972 - 108 = 864 cm²

learn more on trapezium here: brainly.com/question/11961445

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36 cm^2

Step-by-step explanation:

Small window

Length: 2cm

Width: 2cm

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Length: 4cm

Width: 3cm

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