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2 years ago

The surface areas of two similar hexagonal prisms are 882cm² and 1,058 cm²? What is the scale factor of the smaller

Mathematics

1 answer:

max2010maxim [7]2 years ago

7 0

Answer:

scale factor of the smaller prism to the larger prism is B. 21/23

Step-by-step explanation:

Given

surface areas of two similar hexagonal prisms are 882cm² and 1,058 cm²?

scale factor is ratio of sides of two similar objects

thus scale factor for given prism will be = side of smaller prism / side of larger prism

in general rule

If shape of solid has scale factor of k

scale factor of area = k²

scale factor of volume = k³

_____________________________

Given in the problem area of two prism is given

we know area = side^2

scale factor of area = k²

k^2 = area of smaller prism / area of larger prism

$k^2 = 882 / 1058 = 441/529\\k = \sqrt{ 441/529} \\k = 21/23$

Thus, correct option is B 21/23.

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Work out the value of A

Mkey [24]

Answer:

that is really so difficult ? what do you not understand here ? please let me know, if you need any further explanations.

you know what the perimeter is ? if it's the circumference, the way around the object. in other words, the distance you have to walk, when going along all sidelines of the object.

so the perimeter is the sum of of all side lengths.

56 = x - 1 + 3x + 3x + 1 = 7x

x = 8

that gives us the side lengths :

x - 1 = 7 cm

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the formula for the area of a triangle

A = baseline × height / 2

the advantage of a right-angled triangle in this regard is that the sides enclosing the 90 degree angle are already "acting" as baseline and the height (standing on the baseline with a 90 degree angle).

so, we can simply say here, the 3x side is the baseline, and the x-1 side is also the height.

therefore,

A = 21×7/2 = 147/2 = 73.5 cm²

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