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The compound shape below is formed from rectangle ABDE and right-angled triangle

BCD.
What is the area of this shape?
Give your answer in cm' and give any decimal answers to 1 d.p.
A
4cm
B
15 cm
9 cm
E
4 cm
D

The compound shape below is formed from rectangle ABDE and right-angled triangle BCD-example-1
User SMAKSS
by
9.3k points

1 Answer

3 votes

Answer:

90.0 cm²

Explanation:

You want to know the area of the composite figure shown.

Dimensions

The vertical side and hypotenuse of the right triangle are 9 cm and 15 cm. These have the ratio 9/15 = 3/5, so we know this triangle is a 3-4-5 right triangle with a scale factor of 3. The missing side length is 3·(4 cm) = 12 cm.

Area

So, the figure is a trapezoid with a top base of 4 cm, a bottom base of 4+12 = 16 cm, and a height of 9 cm. Its area is ...

A = 1/2(b1 +b2)h

A = 1/2(4 cm +16 cm)(9 cm)

A = 90 cm²

The area of the figure is 90.0 cm².

__

Additional comment

In case you don't recognize the 3:4:5 side ratio, you can figure the base of the triangle using the Pythagorean theorem:

a² +b² = c²

a² = c² -b² = 15² -9² = 225 -81 = 144

a = √144 = 12 . . . . . length of CD in cm

Other useful Pythagorean triples you will see are {5, 12, 13}, {7, 24, 25}, {8, 15, 17}.

User Kyle Finley
by
8.3k points