Respuesta :

Aisin

a) Because it is an equilateral triangle, all the sides must have equal lengths.

The perimeter = 24cm -> Each side = 8.
Area = 1/2 b.h = 8.8.1/2 = 32 cm2.

b) A square has all of its sides of equal lengths just like an equilateral triangle.

The perimeter = 24cm -> Each side = 6.
Area = side.side = 6.6 = 36 cm2.

c) Since they have equal perimeters and the same properties (all sides equal) BUT they have different number of sides and lengths, they won't have the same areas.

d) A rectangle. E.g :
A set of lengths of 5cm and 7cm makes a rectangle with a perimeter of 24cm : (5+7).2

But, its area equals 5 x 7 = 35cm2, which is greater than the triangle.

devishri1977

Answer:

a) 27.71 cm²

b) 36 cm²

Step-by-step explanation:

a) Perimeter of equilateral triangle = 3a

Here, a is the side of equilateral triangle.

Perimeter of equilateral triangle = 24 cm

                   3a = 24 cm

                    a = 24 ÷ 3

                    a = 8 cm

[tex]\sf Area \ of \ equilateral \ traingle = \dfrac{\sqrt{3}}{4}a^2[/tex]

                                         [tex]\sf = \dfrac{\sqrt{3}}{4}*8*8\\\\ = 1.732*2*8\\\\ = 27.71 \ cm^2[/tex]

b)   Perimeter of square = 4s

Here, s is the side of square.

Perimeter of square = 24 cm

                         4s = 24

                           s = 24 ÷ 4

                           s = 6 cm

Area of square = s*s

                         = 6 * 6

                         = 36 cm²

c)  When the dimensions (length, width, height) of the shape changes, the area and volume changes.

d) Length of the rectangle is 10 cm and width is 2 cm.

Perimeter of rectangle = 2*length + 2* width

                                      = 2*10 + 2*2

                                       = 20 + 4

                                       = 24 cm

Area of perimeter of rectangle = length *width

                                                   = 10 * 2

                                                   = 20 cm²

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