Scale Drawings (Copy)
1.
On a scale drawing, 1 cm represents 100 m. A field measures 400 m by 300 m.
(a) Draw the scale rectangle.
(b) Find its area on the drawing.
2.
A road 2.5 km long is drawn using a scale of 1 cm : 500 m.
(a) How many cm long is the road on the drawing?
(b) If extended by 1 km, what will be the new drawing length?
3.
A map uses a scale of 1 : 50 000. The distance between Town A and Town B is 9 cm on the map.
(a) Find the actual distance in km.
4.
A playground is 120 m long and 80 m wide. It is drawn to a scale of 1 : 200.
(a) Draw the rectangle to scale.
(b) Find the perimeter in the real playground.
5.
A plan of a house uses scale 1 cm : 2 m.
(a) Draw a room that measures 6 m × 4 m.
(b) What is the scale area of the room?
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
6.
A map scale is 1 : 25 000.
(a) A straight road is 15 km long. How long is it on the map?
(b) A lake measures 8 cm by 6 cm on the map. Find its actual area in km².
7.
On a scale drawing, 1 cm = 5 m.
A garden path is 35 m long. Draw it to scale.
8.
Two towns, A and B, are 12 km apart. On a map, the scale is 1 : 200 000.
(a) What is their distance in cm on the map?
9.
On a scale of 1 : 1000, a rectangle measures 12 cm by 8 cm on the drawing.
(a) Find the actual dimensions.
(b) Find the actual area.
10.
A rectangular swimming pool is 25 m by 10 m. Draw it to scale 1 cm : 5 m.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
11.
Point A is due north of point B. The bearing of A from B is 000°.
What is the bearing of B from A?
12.
The bearing of Town C from Town D is 065°.
Find the bearing of D from C.
13.
A ship sails from port E to port F on a bearing of 120°.
(a) State the direction of travel (e.g., SE).
(b) Find the bearing of E from F.
14.
Point G is due west of point H.
(a) State the bearing of G from H.
(b) State the bearing of H from G.
15.
A plane flies from airport J to airport K on a bearing of 250°.
Find the bearing of J from K.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
16.
On a scale drawing, 1 cm : 10 m.
A car park is 60 m by 40 m.
(a) Draw it to scale.
(b) Find the real perimeter.
17.
On a map with scale 1 : 100 000, two villages are 7 cm apart.
Find the actual distance in km.
18.
On a map with scale 1 : 25 000, a park is drawn as a rectangle 6 cm by 4 cm.
Find its actual area in hectares. (1 ha = 10 000 m²)
19.
Point L is north-east of point M. The bearing of L from M is 045°.
Find the bearing of M from L.
20.
Point P is south of Q. The bearing of P from Q is 180°.
Find the bearing of Q from P.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
21.
On a school plan, 1 cm = 1.5 m.
A classroom measures 7.5 m by 6 m.
Draw it to scale.
22.
A rectangular park measures 200 m × 150 m.
Draw it on scale 1 cm : 50 m.
23.
On a map, two towns are 15 cm apart. The scale is 1 : 100 000.
Find the real distance in km.
24.
On a map with scale 1 : 5000, a garden measures 4 cm by 3 cm.
Find its real area in m².
25.
A ship sails from point R to point S on a bearing of 070°.
Find the bearing of R from S.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
26.
On a scale 1 cm : 20 m, a sports field is 120 m long.
(a) Draw its scale length.
(b) If width is 60 m, draw to scale and calculate area.
27.
Two cities are 22.5 km apart. On a map, they are 9 cm apart.
Find the scale of the map as a ratio.
28.
Point T is due east of U.
(a) Find the bearing of T from U.
(b) Find the bearing of U from T.
29.
A plane travels from V to W on a bearing of 315°.
Find the bearing of V from W.
30.
On a town plan, scale 1 cm = 50 m.
A shopping mall measures 150 m × 100 m.
(a) Draw it to scale.
(b) Find its perimeter in the real world.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
1.
Scale: 1 cm : 100 m.
400 m → 4 cm, 300 m → 3 cm.
Area on drawing = 4 × 3 = 12 cm².
2.
1 cm = 500 m.
2.5 km = 2500 m → 2500 ÷ 500 = 5 cm.
Extra 1 km = 1000 ÷ 500 = 2 cm.
New length = 7 cm.
3.
1 : 50 000 → 1 cm = 0.5 km.
9 cm = 9 × 0.5 = 4.5 km.
4.
1 : 200 → 1 cm = 200 m.
120 m → 0.6 cm, 80 m → 0.4 cm.
Real perimeter = 2(120+80) = 400 m.
5.
1 cm : 2 m.
6 m → 3 cm, 4 m → 2 cm.
Scale area = 3 × 2 = 6 cm².
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
6.
(a) 15 km = 15 000 m. Scale 1 : 25 000 → 1 cm = 250 m.
15 000 ÷ 250 = 60 cm.
(b) 8 cm × 6 cm = 48 cm² on map. Scale factor (250 m)² = 62 500 m² per cm².
Actual area = 48 × 62 500 = 3 000 000 m² = 3 km².
7.
1 cm = 5 m.
35 m → 35 ÷ 5 = 7 cm.
8.
Scale 1 : 200 000.
12 km = 1 200 000 cm.
On map = 1 200 000 ÷ 200 000 = 6 cm.
9.
Scale 1 : 1000.
12 cm = 12 000 cm = 120 m, 8 cm = 80 m.
Area = 120 × 80 = 9600 m².
10.
1 cm = 5 m.
25 m = 5 cm, 10 m = 2 cm.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
11.
Bearing A from B = 000°.
Bearing B from A = 180°.
12.
C from D = 065°.
So D from C = 065 + 180 = 245°.
13.
E → F on 120° (South-East).
F → E = 120 + 180 = 300°.
14.
G from H = 270°.
H from G = 090°.
15.
J → K = 250°.
K → J = 070°.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
16.
1 cm : 10 m.
60 m → 6 cm, 40 m → 4 cm.
Perimeter real = 200 m.
17.
1 cm = 1 km.
7 cm = 7 km.
18.
1 : 25 000 → 1 cm = 250 m.
6 cm → 1500 m, 4 cm → 1000 m.
Area = 1.5 × 1 = 1.5 km² = 150 ha.
19.
L from M = 045°.
M from L = 225°.
20.
P from Q = 180°.
Q from P = 000°.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
21.
1 cm = 1.5 m.
7.5 m → 5 cm, 6 m → 4 cm.
22.
1 cm : 50 m.
200 m → 4 cm, 150 m → 3 cm.
23.
1 : 100 000.
15 cm = 15 × 1 km = 15 km.
24.
1 : 5000 → 1 cm = 50 m.
4 cm = 200 m, 3 cm = 150 m.
Area = 200 × 150 = 30 000 m².
25.
R from S = 070°.
S from R = 250°.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
26.
1 cm : 20 m.
120 m → 6 cm, 60 m → 3 cm.
Area = 120 × 60 = 7200 m².
27.
22.5 km = 2 250 000 cm.
Scale = 2 250 000 ÷ 9 = 250 000.
So scale 1 : 250 000.
28.
T from U = 090°.
U from T = 270°.
29.
V → W = 315°.
W → V = 135°.
30.
1 cm = 50 m.
150 m → 3 cm, 100 m → 2 cm.
Real perimeter = 2(150+100) = 500 m.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course