In the figure AB=20m,BC=21m,AD=20 and DE=10.5.Find the area of the shaded region
Answers
Answer:
In the diagram AB=20 cm, BC=21 cm, AD=10cm and DE=10.5cm?
Angles ABC and ADE are right angles. If triangle ADE is removed from triangle ABC, what is the area of the shaded region that remains? The shaded area being BCED.
The area of a triangle is given by: ½ the base x the vertical height.
The area of triangle ABC = (1/2 x BC) x AB
= (1/2 x 21cm) x 20cm
= 10.5cm x 20cm
= 210 cm^2
The area of triangle ADE = (1/2 x DE) x AD
= (1/2 x 10.5cm) x 10cm
= 5.25cm x 10cm
= 52.5 cm^2
Subtracting the area of ADE from the area of ABC gives the area of BCED.
210 cm^2 – 52.5 cm^2 = 157.5 cm^2
You may also notice that these 2 triangles have special properties. They are “similar” triangles and as side AD is ½ side AB, DE will be ½ BC and ADE will fit 4 times into ABC.