Area P5 2010 CA2

The attached figure is made up of two pairs of identical squares of different sizes. DCG is a straight line. The sum of the area of 1 large square and 1 small square is 52 cm2.

(a) What is the area of the shaded portion?

(b) What is the ratio of the area of triangle AHC to the area of triangle ACG?
 
 
As we may not know that 52 = 16 + 36 = (4 x 4) + (6 x 6), we will list out L x L, then look out for sum of two of the multiples that equals to 52.
L       --> 1 , 2 , 3 ,  4  .  5  ,  6
L x L --> 1 , 4 , 9 , 16 , 25 , 36
 
16 + 36 = 52    So sides of squares are 4 cm and 6 cm
 
1/2 x 4 x 6 = 12
 
12 x 2 = 24 cm2
 
a) The area of the shaded portion is 24 cm2.
 
 
1/2 x 12 x 6 = 36
 
36 : 12 = 3 : 1
 
b) The ratio of the area of triangle AHC to the area of ACG is 3 : 1.
 
 
Short cut for b) is as follows:
 
2 x 6 : 4 = 3 : 1 [Height1 : Height 2 since Base the same]

Area P5 A003

Two identical right-angled triangles overlapped each other as shown in the diagram below. Find the area of the shaded part.

3.5 x 11 = 38.5 (Area of Parallelogram ABCD)

1/2 x 3.5 x 5 = 3.85 (Area of Trianlge ADE)

38.5 - 3.85 = 29.75 cm²

The area of the shaded part is 29.75 cm².

Area P5 A002

The area of rectangle ABCD below is 140 cm². Area of triangle XYD is 20 cm2. Find the total shaded area of the rectangle.

140 ÷ 2 = 70

140 – 70 – 20 = 50 cm²

The total shaded area of the rectangle is 50 cm².

Area P5 A001

Mr Huang knocked 160 nails along the perimeter of the ceiling of a function room measuring 20 m long by 12 m wide. The distance between each nail was equal. He hung 3 balloons on each nail.

(a) How many nails were knocked along the width of the ceiling?

(b) How many balloons did he buy in all if he has 20 left?

20 + 12 = 32

32 x 2 = 64 m (Perimeter of ceiling)

160/64 = 2.5 (Number of nails per metre)

2.5 x 12 = 30

30 + 1 = 31 (Nails from one corner of the width to the other)

31 x 2 = 62 nails (The ceiling has 2 width)

a)  62 nails were knocked along the width of the ceiling.

160 x 3 = 480

480 + 20 = 500 balloons

b) He bought 500 balloons. 

Area P5 2009 SA1 P2 MGS Q3

3. In the diagram below, ABCD is a square. AC = 18 cm. Find the area of the triangle ABC.

Area of triangle ABC = ½ x 18 x (½ x 18).
1/2 x 18 x 1/2 x 18 = 81 cm²