(b) 1 = 2 dm; b=1 dm; h=0,75 dm photo answers
Answers
Answer:
is important to be able to measure and calculate surface areas. It might be necessary to calculate, for example, the surface area of the cross-section of a canal or the surface area of a farm.
This Section will discuss the calculation of some of the most common surface areas: the triangle, the square, the rectangle, the rhombus, the parallelogram, the trapezium and the circle (see Fig. 1a).
Fig. 1a. The most common surface areas
The height (h) of a triangle, a rhombus, a parallelogram or a trapezium, is the distance from a top corner to the opposite side called base (b). The height is always perpendicular to the base; in other words, the height makes a "right angle" with the base. An example of a right angle is the corner of this page.
In the case of a square or a rectangle, the expression length (1) is commonly used instead of base and width (w) instead of height. In the case of a circle the expression diametre (d) is used (see Fig. 1b).
Fig. 1b. The height (h), base (b), width (w), length (1) and diametre (d) of the most common surface areas
1.1.1 Triangles
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