PREPARED BY MRS ASSUMPTA KASAMBA@MATHSDEPTGHS 0772937519 1 1 MENSURATION(part1) GAYAZA HIGH SCHOOL S4 MATHEMATICS ( MAY)2020 Mensuration is the branch of mathematics which studies the measurement of the geometric shapes and the calculation of their parameters like area, perimeter, surface area, volume etc. Types of Mensuration Plane mensuration deals with the sides, perimeters and areas of plane figures of different shapes. Solid mensuration deals with the surface areas and volumes of solid objects. The shapes exist in either 2 dimensions (2D) or 3 dimensions (3D). Differences between 2D and 3D shapes 2D shape 3D shape This is a shape surrounded by three or more straight lines in a plane. These shapes are plane figures such as the triangle, square, rectangle, trapezium, parallelograms , rhombus ,kite , circle etc. These shapes have lengths in two directions . We can measure and calculate their area and perimeter This is a shape surrounded by a number of surfaces or planes. These shapes are called solids such as the prisms( cube,cuboid, cylinder , triangular , etc ),cone,sphere , pyramids etc These shapes have lengths in three different directions. We can measure and calculate their volume and total surface area. AREA OF TRIANGLE: Area of triangle when given the base and the perpendicular height. Find the area of the following triangles 8cm 10cm 20cm 12cm 9cm 16cm 3.2 m 4.5 m
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MENSURATION(part1)...Mensuration is the branch of mathematics which studies the measurement of the geometric shapes and the calculation of their parameters like area, perimeter, surface
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PREPARED BY MRS ASSUMPTA KASAMBA@MATHSDEPTGHS 0772937519 1
1 MENSURATION(part1)
GAYAZA HIGH SCHOOL
S4 MATHEMATICS ( MAY)2020
Mensuration is the branch of mathematics which studies the measurement of the geometric
shapes and the calculation of their parameters like area, perimeter, surface area, volume etc.
Types of Mensuration
Plane mensuration deals with the sides, perimeters and areas of plane figures of
different shapes.
Solid mensuration deals with the surface areas and volumes of solid objects.
The shapes exist in either 2 dimensions (2D) or 3 dimensions (3D).
Differences between 2D and 3D shapes
2D shape 3D shape
This is a shape surrounded by three
or more straight lines in a plane.
These shapes are plane figures such
as the triangle, square, rectangle,
trapezium, parallelograms , rhombus
,kite , circle etc.
These shapes have lengths in two
directions .
We can measure and calculate their
area and perimeter
This is a shape surrounded by a number of
surfaces or planes.
These shapes are called solids such as the
prisms( cube,cuboid, cylinder , triangular , etc
),cone,sphere , pyramids etc
These shapes have lengths in three different
directions.
We can measure and calculate their volume and
total surface area.
AREA OF TRIANGLE:
Area of triangle when given the base and the perpendicular height.
Find the area of the following triangles
8cm 10cm 20cm
12cm
9cm
16cm
3.2 m
4.5 m
PREPARED BY MRS ASSUMPTA KASAMBA@MATHSDEPTGHS 0772937519 2
2 MENSURATION(part1)
In addition to the formula π¨πππ ππ ππππππππ = π
πππ , there are two other useful formulae
Area of a triangle when two sides and an included angle are given
2. In a fitness exercise, students run round the three sides of a triangular field
PQR. Given that ππ = 95π, ππ = 120π and ππ = 145π. Find the area
of the field.
3. A fishing boat travelled 3.2km from a lighthouse L to a point M. It then
travelled from M to a point N and then back to the lighthouse. If
ππ = 1.7ππ, πΏπ = 2.8ππ, find the area covered by the boat.
4. A farmer marks off a triangular piece of land for growing vegetables. Given
that π΄π΅ = 39.5π, π΅πΆ = 68.6π and < π΄π΅πΆ = 43Β°, calculate the area of the
piece of land.
5. In an isosceles triangle ABC in which π΄π΅ = 12ππ, π΄πΆ = π΅πΆ = π₯ππ and angle
π΄πΆπ΅ = 120Β°. Find the (a) value of x (b)area of the triangle
PREPARED BY MRS ASSUMPTA KASAMBA@MATHSDEPTGHS 0772937519 4
4 MENSURATION(part1)
Further worked examples
Example 1 In the given triangle ABC, the shaded area is 20cπ2. Given that π΄πΆ = 10ππ, π΅π = π₯ππ and ππΆ = 2π₯ cm , find the area of the unshaded region.
Example 2 In the figure ABCD is a rectangle in which AD= 5π₯ ππ and AB= 3π₯ ππ. M and N are the mid points of BC and CD respectively.