Geometrical Constructions (Copy)
1.
Construct a triangle ABC such that AB = 7 cm, BC = 6 cm and AC = 5 cm using a ruler and compasses.
(a) Show all construction arcs.
(b) Measure ∠ABC to the nearest degree.
2.
Construct a triangle PQR with PQ = 8 cm, QR = 5 cm and PR = 7 cm.
(a) Draw the triangle using compasses and ruler only.
(b) Find the area of the triangle using ½ab sinC.
3.
Draw the net of a cube of side 4 cm.
(a) Construct it clearly with ruler and compasses.
(b) Calculate its total surface area.
4.
Draw the net of a cuboid measuring 6 cm × 4 cm × 3 cm.
(a) Show all dimensions.
(b) Calculate its volume.
5.
Construct an equilateral triangle XYZ with each side 6 cm.
(a) Show all arcs.
(b) Find the size of each angle.
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.
Draw the net of a square-based pyramid with base 5 cm and slant edge 8 cm.
(a) Show all triangular faces.
(b) Calculate the total surface area.
7.
Construct a rhombus with side 6 cm and one diagonal 8 cm.
(a) Show arcs used.
(b) Measure one of the angles.
8.
Construct a triangle DEF such that DE = 10 cm, EF = 7 cm and DF = 9 cm.
(a) Draw it accurately.
(b) Measure angle DEF.
9.
Draw the net of a triangular prism with triangular cross-section sides 5 cm, 5 cm, 6 cm and prism length 8 cm.
(a) Show all faces clearly.
(b) Find its surface area.
10.
Draw the net of a cone with radius 3 cm and slant height 5 cm.
(a) Show the circular base and curved surface sector.
(b) Find the curved surface area.
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.
Construct an isosceles triangle GHI with GH = HI = 6 cm and GI = 8 cm.
(a) Show arcs used.
(b) Measure the vertex angle.
12.
Construct a scalene triangle JKL with sides 5 cm, 7 cm, and 9 cm.
(a) Draw arcs.
(b) Measure the largest angle.
13.
Construct a rectangle MNPQ with MN = 8 cm, NP = 5 cm.
(a) Show construction.
(b) Draw its diagonal and measure it.
14.
Draw the net of a cylinder with radius 3 cm and height 7 cm.
(a) Show the two circles and rectangle.
(b) Find its surface area.
15.
Construct a kite RSTU with sides RS = RU = 6 cm, ST = 4 cm.
(a) Show arcs.
(b) Measure ∠RSU.
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.
Construct â–³VWX with VW = 9 cm, WX = 5 cm, VX = 7 cm.
(a) Draw arcs.
(b) Find area by Heron’s formula.
17.
Draw the net of a hexagonal prism with hexagonal base side 3 cm and prism length 7 cm.
(a) Show all 8 faces.
(b) Calculate total surface area.
18.
Draw the net of a square-based prism with base 4 cm × 4 cm and prism length 10 cm.
(a) Show faces.
(b) Find volume.
19.
Construct a trapezium ABCD with AB = 8 cm, CD = 5 cm, AD = BC = 4 cm.
(a) Show arcs.
(b) Measure ∠BAD.
20.
Construct â–³XYZ with XY = 6 cm, YZ = 7 cm, ZX = 8 cm.
(a) Show arcs.
(b) Measure ∠XYZ.
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.
Construct a triangle with sides 4 cm, 5 cm, 6 cm.
(a) Show arcs.
(b) Find perimeter.
22.
Draw the net of a triangular pyramid with base sides 5 cm, 6 cm, 7 cm.
(a) Show triangular faces.
(b) Find surface area.
23.
Draw the net of a cuboid 12 cm × 6 cm × 4 cm.
(a) Label dimensions.
(b) Find surface area.
24.
Construct an isosceles triangle with base 10 cm and equal sides 7 cm.
(a) Show arcs.
(b) Measure vertex angle.
25.
Draw the net of a cylinder with radius 5 cm and height 12 cm.
(a) Show circular bases and rectangle.
(b) Find surface area.
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.
Construct a rhombus with side 5 cm and one diagonal 8 cm.
(a) Show arcs.
(b) Measure one angle.
27.
Draw the net of a cone with radius 4 cm and slant height 9 cm.
(a) Show base and sector.
(b) Find curved surface area.
28.
Construct â–³PQR with PQ = 9 cm, PR = 6 cm, QR = 5 cm.
(a) Show arcs.
(b) Find area.
29.
Draw the net of a cube with side 3 cm.
(a) Label all edges.
(b) Find its surface area.
30.
Construct â–³ABC with AB = 5 cm, AC = 7 cm, BC = 8 cm.
(a) Show arcs.
(b) Measure ∠ABC.
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.
Triangle with AB = 7 cm, BC = 6 cm, AC = 5 cm.
- Construct base AB = 7 cm.
- With compass, arc from A radius 5 cm, arc from B radius 6 cm, intersection = C.
- Join AC, BC.
- ∠ABC ≈ 43°.
2.
PQ = 8 cm, QR = 5 cm, PR = 7 cm.
- Construct base PQ = 8 cm.
- Arc from P radius 7 cm, arc from Q radius 5 cm, meet at R.
- Area = ½ × 8 × 5 × sinθ. θ = ∠PQR ≈ 39°.
- Area ≈ 25.3 cm².
3.
Cube net: 6 equal squares of side 4 cm arranged in cross pattern.
- TSA = 6 × 4² = 96 cm².
4.
Cuboid net: 3 pairs of rectangles (6×4, 6×3, 4×3).
- Volume = 6×4×3 = 72 cm³.
5.
Equilateral triangle side 6 cm.
- Compass arc from A and B radius 6 cm, intersection C.
- Join AC, BC.
- Angles = 60° each.
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.
Square base pyramid, base side 5 cm.
- Draw square base.
- From each corner, construct isosceles triangles with slant edge 8 cm.
- TSA = base area + 4 × area of triangle = 25 + 4×(½×5×√(8²–2.5²)) = 25 + 4×19.8 ≈ 104.
7.
Rhombus side 6 cm, diagonal 8 cm.
- Draw diagonal 8 cm.
- Use compass radius 6 cm from both ends of diagonal, mark intersections = other vertices.
- One angle ≈ 82°.
8.
Triangle DEF: DE = 10, EF = 7, DF = 9.
- Construct with arcs.
- ∠DEF ≈ 44°.
9.
Triangular prism: base triangle sides 5,5,6.
- Net: two triangles + 3 rectangles.
- Surface area ≈ 2×(12 cm²) + (5+5+6)×8 = 24 + 128 = 152 cm².
10.
Cone net: base circle radius 3 cm + sector radius 5 cm.
- Curved surface area = πrs = π×3×5 = 47.1 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
11.
Isosceles triangle GH = HI = 6 cm, GI = 8 cm.
- Construct GI = 8 cm.
- Arcs from G and I radius 6 cm intersect at H.
- Vertex angle ≈ 104°.
12.
Scalene 5,7,9.
- Construct with arcs.
- Largest angle opposite side 9 cm ≈ 113°.
13.
Rectangle 8×5 cm.
- Diagonal = √(8²+5²) = √89 ≈ 9.4 cm.
14.
Cylinder net: 2 circles radius 3 cm + rectangle 7×circumference.
- Rectangle length = 2Ï€r = 18.8 cm.
- Surface area = 2πr² + 2πrh = 2π(9) + 2π(21) ≈ 188.4 cm².
15.
Kite RS=RU=6, ST=4.
- Construct triangle with equal sides.
- ∠RSU ≈ 66°.
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.
VW=9, WX=5, VX=7.
- Construct with arcs.
- Area by Heron: s=10.5, area = √(10.5(1.5)(5.5)(3.5)) ≈ 17.4 cm².
17.
Hexagonal prism: 2 hexagons + 6 rectangles.
- Base area = 6×½×3×2.6 ≈ 23.4.
- TSA ≈ 2×23.4 + 6×3×7 ≈ 164 cm².
18.
Square-based prism: base 4×4, length 10.
- Net = 2 squares + 4 rectangles.
- Volume = 16×10 = 160 cm³.
19.
Trapezium: AB=8, CD=5, AD=BC=4.
- Construct with arcs.
- ∠BAD ≈ 76°.
20.
Triangle 6,7,8.
- Construct with arcs.
- ∠XYZ ≈ 75°.
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.
Triangle 4,5,6.
- Construct arcs.
- Perimeter = 15 cm.
22.
Triangular pyramid base 5,6,7.
- Net: 4 triangles.
- Surface area ≈ 72 cm².
23.
Cuboid 12×6×4.
- TSA = 2(lw+lh+wh) = 2(72+48+24) = 288 cm².
24.
Isosceles with base 10, sides 7.
- Vertex angle ≈ 94°.
25.
Cylinder radius 5, height 12.
- Net = 2 circles + rectangle 12×31.4.
- TSA = 2πr²+2πrh = 2π(25)+2π(60) ≈ 565.5 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
26.
Rhombus side 5, diagonal 8.
- Construct with arcs.
- Angle ≈ 53°.
27.
Cone radius 4, slant 9.
- Sector radius 9, arc length 2Ï€r=25.1.
- Curved area = πrs = 113.1 cm².
28.
Triangle 9,6,5.
- Construct.
- Area by Heron = 14 cm².
29.
Cube side 3.
- TSA = 6×9 = 54 cm².
30.
Triangle 5,7,8.
- Construct arcs.
- ∠ABC ≈ 78°.
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