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3 years ago

The surface area of a triangle pyramid is 1,936mm2. If the dimensions are multiplied by 1/4 what will be the new surface area?

Mathematics

1 answer:

Mumz [18]3 years ago

4 0

Answer:

The new surface area will be $121\ mm^{2}$

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared

In this problem

The scale factor is $\frac{1}{4}$

Multiply the scale factor squared by the original surface area to obtain the new surface area

$(\frac{1}{4})^{2}*1,936=121\ mm^{2}$

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Step-by-step explanation:

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radius= 6 units

Let's find the length between each points to see which is equal to 6 units, using the distance formula below.

$distance = \sqrt{(y1 - y2)^{2} + {(x1 - x2)}^{2} }$

A. Distance between 2 points

$= \sqrt{ {(10 + 5)}^{2} + ( - 2 + 6)^{2} } \\ = \sqrt{15 ^{2} + {4}^{2}} \\ = \sqrt{241} \\ = 15.524 \: units$

(to 5 s.f.)

Since the distance is greater than 6 units, point A lies outside the circle.

B. Distance between 2 points

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Since the distance of B from the center is 6 units, point B lies on Circle O.

Let's check the other 2 points:

C. Distance between 2 points

$= \sqrt{ {(10 - 4)}^{2} + {( - 2 - 6)}^{2} } \\ = \sqrt{ {6}^{2} + ( - 8)^{2} } \\ = \sqrt{100} \\ = 10 \: units$

Since the distance of point C from the center is greater than 6 units, point C lies outside the circle.

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