Example 1 :
Triangle DEC has area 4.2 cm2.
a) Find the area of triangle ABC.
b) Find the area of quadrilateral ABED.
In the triangle given above, ΔABC and ΔDEC.
<BCA = <ECD (A)
ABC = <EDC (A)
ΔABC and ΔDEC are similar. Bases of triangle ABC and EDC are BC and DC respectively.
(i) Area of Δ ABC/Area of Δ DEC = (BC/DC)2
Area of Δ ABC/4.2 = (6/4)2
Area of Δ ABC = (36/16) x 4.2
= 9.45 cm2
(ii) Area of quadrilateral AEBD = Area of triangle ABC - Area of triangle DEC
= 5.25 cm2
So, area of quadrilateral is AEBD is 5.25 cm2.
Example 2 :
If triangle ABC has area 15 cm2:
a) find the area of ΔCDE
b) find the area of PQED.
(a) In triangles ABC and CDE
AB is parallel to DE
Area of ABC/Area of CDE = (AB/DE)2
15/Area of CDE = (5/8)2
15/Area of CDE = 25/64
Area of CDE = 15(64)/25
= 38.4 cm2
In triangles CPQ and CDE
PQ is parallel to DE
Area of ΔCPQ/area of ΔCDE = (CQ/CE)2
CQ = x and CE = 2x
Area of ΔCPQ/38.4 = (x/2x)2
Area of ΔCPQ = 38.4/4
Area of ΔCPQ = 9.6
(b) Area of quadrilateral DPQE
= Area of CDE - Area of CPQ
= 28.8 cm2
Example 3 :
What will happen to the volume of:
a) a sphere if the radius is doubled
b) a sphere if the radius is increased by 20%
Volume of sphere = (4/3)πr3
(a) Radius of the sphere = r
Radius of new sphere = 2r
Volume of new sphere = (4/3)π(2r)3
= 8 x (4/3)πr3
So, volume of the new sphere will be 8 times volume of old sphere.
(b) Radius of sphere is increased by 20%.
Radius of new sphere = 1.20r
Volume of new sphere = (4/3)π(1.20r)3
= 1.728 x (4/3)πr3
So, volume of the new sphere will be 1.728 times volume of old sphere.
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