Which of the following has the formula length x breadth x height ?
Answers
Answer:
The surface area or surface (A) of a triangle is calculated by the formula:
A (triangle) = 0.5 x base x height = 0.5 x b x h ..... (1)
Triangles can have many shapes (see Fig. 2) but the same formula is used for all of them.
Fig. 2. Some examples of triangles
EXAMPLE
Calculate the surface area of the triangles no. 1, no. 1a and no. 2
Given
Answer
Triangles no. 1 and no. 1a:
base = 3 cm
height = 2 cm
Formula:
A = 0.5 x base x height
= 0.5 x 3 cm x 2 cm = 3 cm2
Triangle no. 2:
base = 3 cm
height = 2 cm
A = 0.5 x 3 cm x 2 cm = 3 cm2
It can be seen that triangles no. 1, no. 1a and no. 2 have the same surface; the shapes of the triangles are different, but the base and the height are in all three cases the same, so the surface is the same.
The surface of these triangles is expressed in square centimetres (written as cm2). Surface areas can also be expressed in square decimetres (dm2), square metres (m2), etc...
QUESTION
Calculate the surface areas of the triangles nos. 3, 4, 5 and 6.
Given
Answer
Triangle no. 3:
base = 3 cm
height = 2 cm
Formula:
A = 0.5 x base x height
= 0.5 x 3 cm x 2 cm = 3 cm2
Triangle no. 4:
base = 4 cm
height = 1 cm
A = 0.5 x 4 cm x 1 cm = 2 cm2
Triangle no. 5:
base = 2 cm
height = 3 cm
A = 0.5 x 2 cm x 3 cm = 3 cm2
Triangle no. 6:
base = 4 cm
height = 3 cm
A = 0.5 x 4 cm x 3 cm = 6 cm2
1.1.2 Squares and Rectangles
The surface area or surface (A) of a square or a rectangle is calculated by the formula:
A (square or rectangle) = length x width = l x w ..... (2)
In a square the lengths of all four sides are equal and all four angles are right angles.
In a rectangle, the lengths of the opposite sides are equal and all four angles are right angles.
Fig. 3. A square and a rectangle
Note that in a square the length and width are equal and that in a rectangle the length and width are not equal (see Fig. 3).
QUESTION
Calculate the surface areas of the rectangle and of the square (see Fig. 3).
Given
Answer
Square:
length = 2 cm
width = 2 cm
Formula:
A = length x width
= 2 cm x 2 cm = 4 cm2
Rectangle:
length = 5 cm
width = 3 cm
Formula:
A = length x width
= 5 cm x 3 cm = 15 cm2
Related to irrigation, you will often come across the expression hectare (ha), which is a surface area unit. By definition, 1 hectare equals 10 000 m2. For example, a field with a length of 100 m and a width of 100 m2 (see Fig. 4) has a surface area of 100 m x 100 m = 10 000 m2 = 1 ha.
Fig. 4. One hectare equals 10 000 m2
1.1.3 Rhombuses and Parallelograms
The surface area or surface (A) of a rhombus or a parallelogram is calculated by the formula:
A (rhombus or parallelogram) = base x height = b x h ..... (3)
In a rhombus the lengths of all four sides are equal; none of the angles are right angles; opposite sides run parallel.
In a parallelogram the lengths of the opposite sides are equal; none of the angles are right angles; opposite sides run parallel (see Fig. 5).
Fig. 5. A rhombus and a parallelogram
QUESTION
Calculate the surface areas of the rhombus and the parallelogram (see Fig. 5).
Given
Answer
Rhombus:
base = 3 cm
height = 2 cm
Formula:
A = base x height
= 3 cm x 2 cm = 6 cm2
Parallelogram:
base = 3.5 cm
height = 3 cm
Formula:
A = base x height
= 3.5 cm x 3 cm = 10.5 cm2
1.1.4 Trapeziums
The surface area or surface (A) of a trapezium is calculated by the formula:
A (trapezium) = 0.5 (base + top) x height = 0.5 (b + a) x h ..... (4)
The top (a) is the side opposite and parallel to the base (b). In a trapezium only the base and the top run parallel.
Some examples are shown in Fig. 6:
Fig. 6. Some examples of