1. Johny walked in a garden start from point A. Then he walk to the west 14 meters to point B and he turn to the north 48 meters. The last position was named as C. If he want to go to C shortly, how far the distance?

Answer

Start position is A and the last is C. The illustration is

Look at the illustration. It is right triangle then we can use Pythagorean Theorem to determine distance from A to C.

AC = √(14² + 48²)

= √(196+2304)

= √(2500)

= 50 m

So, Johny can walk 50m from A to C.

2. Look at the figure

Determine the degree of a+b.

Answer

a = 8x

b = 6x

the figure is supplementary then the sum of angles is 180°

a + b + a + b + 40° = 180°

8x + 6x + 8x + 6x + 40° = 180°

28x = 140°

x = 5

then a + b = 8x + 6x = 14x = 14(5) = 70°

3. There is a rectangular ABCD. AB = 12 cm, BC is 4/3 of AB. There is a point E 3cm from A and point F 9 cm from D. the center of diagonals is O. Determine the length of FO.

Answer

Illustrate the rectangular

Determining FO will be easier if we create a line from O to the up side of rectangular. Let it be G.

Now, focus on DFOG

FO = √(1.5² + 4.5²)

= √(2.25 + 20.25)

= √22.5

= 15√10

So, FO = 15√10.

4. Determine the area of a rhombus if the perimeter is 20 cm and one of the diagonal is 6 cm.

Answer

Perimeter of rhombus = 4 x sides

20 = 4 x sides

Sides = 5 cm

One of diagonal is 6 cm.

Look at the illustration

Next step is determine length of another diagonal.

Using triple Pythagoras 3, 4, and 5 then it is 4 cm. So, another diagonal is 8 cm.

Area of rhombus = ½ x d1 x d2

= ½ x 6 x 8

= ½ x 48

= 24 cm²

So the area of the rhombus is 24cm².

5. Area of a circle is 50.24 m² (p=3.14). It will be fenced by using iron. If the iron price is $1 then determine how much the cost.

Answer

Area = 50.24

50.24 = pr²

50.24 = 3.14 x r²

r² = 16

r = 4 m

then the circumference = 2pr

= 2 x 3.14 x 4

= 25.12 m

So the total cost is 25.12 x $1 = $25.12.

6. Look at the figure

If the area of triangle is 55 cm² and the length of square is 14cm determine the shaded area.

Answer

The shaded area is area of a circle minus area of triangle.

Area of circle is determined by using length of square as the diameter.

Length of square = diameter = 14 cm. Then radius is 7 cm.

Area of circle = pr²

= 22/7 x 7²

= 154 cm²

Then shaded area = 154 – 55 = 99 cm²