**Question 7 (a)**:

In Diagram 7.1, arcs

*BE*and

*CD*which are centred at

*A,*are the arches of a bridge. The radius used to build arc

*BE*is 8 m.

(i) Calculate the length, in m, of arc

*BE*. Round off the answer to two decimal places.

[Use π = 3.142]

(ii) The length of arc

*CD*is 9.95 m.

Calculate the distance, in m, between arc

*CD*and

*BE*. Round off the answer to two decimal places.

[Use π = 3.142]

**Solution**:**(i)**

$\begin{array}{l}\text{Lengthofarc}BE\\ =\frac{50}{360}\times 2\times 3.142\times 8\\ =6.9822\\ =6.98\text{m}\end{array}$

$\begin{array}{l}\text{Lengthofarc}BE\\ =\frac{50}{360}\times 2\times 3.142\times 8\\ =6.9822\\ =6.98\text{m}\end{array}$

(ii)

(ii)

**$\begin{array}{l}\text{Lengthofarc}CD=9.95\text{m}\\ \frac{50}{360}\times 2\times 3.142\times r=9.95\\ r=\frac{9.95\times 360}{50\times 2\times 3.142}\\ r=11.40\text{m}\\ \\ \text{Distancebetween}CD\text{and}BE\\ =11.40-8\\ =3.40\text{m}\end{array}$**

**Question 7 (b)**:

Diagram 7.2 shows the floor plan for rooms

*P*and

*Q*which are rented by Syarikat Mesra.

(i) State the length, in cm, floor room

*Q*which has been redrawn using scale 1 : 200.

(ii) A rectangular mat with the length of 4 m and the perimeter of 13 m is placed on the floor in room

*P*.

Calculate, in m

^{2}, the area of the floor space of room

*P*that is not covered by the mat.

**Solution**:**(i)**

$\begin{array}{l}\text{Lengthoffloorofroom}Q\\ =\frac{800\text{cm}}{200}\\ =4\text{cm}\end{array}$

**(ii)**

Area of mat = 4 × 2.5

= 10 m

^{2 }Area of room

*P*= 7 m × 5 m

= 35 m

^{2 }Area of floor space of room

*P*that is not covered by the mat

= 35 – 10

= 25 m

^{2}