Figure Measurements

Measurements are used to measure the length of a cloth for stitching, the area of a wall for white washing, the perimeter of a land for fencing and the volume of a container for filling. The measurements consist of lengths, angles, areas, perimeters and volumes of plane and solid figures. If a student wants to know about the measurements of figure, they can be referring the following examples.

Figure Measurements – Examples 1:

These are the examples for measurements of a figure.

figure measurements

Find the area of the triangle whose height is 10cm and base is 6cm.

Solution:

Given base = 6cm

height = 10cm

Area of triangle = `1 / 2 (base xx height)`

= `1 /2 (6 xx 10)`

= `1 / 2 (60)`

= 30

Therefore, the area of the triangle is 30cm2

Find the area of the triangle whose height is 12cm and base is 8cm.

Solution:

Given base = 8cm

height = 12cm

Area of triangle = `1 / 2 (base xx height)`

= `1 /2 (8 xx 12)`

= `1 / 2 (96)`

= 48

Therefore, the area of the triangle is 48cm2

Figure Measurements – Examples 2:

These are the examples for measurements of a figure.

Measurements of Figure 1:

Three angles of a triangle are x + 34˚, x + 40˚ and x + 46˚. We have to find x for the triangle.

Solution:

x + 34 + x +40 + x + 46 = 180˚

The sum of the three angles of a triangle is equal to 180˚

3x + 120 = 180˚

3x = 180˚ - 120˚

= 90˚

x = `60/3`

= 20˚

Measurements of Figure 2:

The triangle has a three angles  x + 20˚, x + 10˚ and x + 30˚. We have to find x for the triangle.

Solution:

x + 20 + x +10 + x + 30 = 180˚

The sum of the three angles of a triangle is equal to 180˚

3x + 60 = 180˚

3x = 180˚ - 60˚

= 120˚

x = `120/3`

= 40˚

Algebra is widely used in day to day activities watch out for my forthcoming posts on Multiplying Mixed Number Fractions and Strategies for Addition. I am sure they will be helpful.

Measurements of Figure 3:

The measurements of the angles whose triangle are in the ratio 2:1:3. Calculate the angles of the given triangle values.

Solution:

Ratio of the angles of a triangle = 2:1:3

Total ratio = 2 + 1 + 3

= 6

Sum of the three angles of a triangle is 180˚. Therefore,

First angle = `2/6 xx 180`

= 60˚

Second angle = `1/6 xx 180`

= 30˚

Third angle = `3/6 xx 180`

= 90˚