Idon't really know how to figure this question

for a regular triangle, find, exactly, its radius, the length of one of its sides, its area, and the areas of the inscribed and circumscribed circles if its apothem is 16.

Step-by-step explanation:

For geometry problems, it is usually helpful to start by making a diagram. In the attached diagram, you are given equilateral triangle ABC and the apothem OX = 16.

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1. Triangle Radius

The length OA is the radius of the triangle (the radius of the circumcircle). Its relation to the apothem is ...

  OX/OA = sin(30°) = 1/2

  OA = 2·OX = 2·16 = 32

The radius of the regular triangle is 32.

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2. Triangle side length

The length AX is half the side length. Its relation to AX is ...

  OX/AX = tan(30°) = (√3)/3

  AX = OX·√3 = 16√3

  AC = 2·AX = 32√3

The side length of the regular triangle is 32√3.

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3. Triangle area

The area formula can be used. We know the side length from part 2. and we know the height of the triangle, BX, is the sum of the radius and the apothem, so is 32+16 = 48.

  Triangle Area = (1/2)bh = (1/2)(32√3)(48) = 768√3

The area of the triangle is 768√3.

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4. Area of Inscribed circle

The radius of the inscribed circle is the apothem, 16. So the circle area is ...

  A = πr² = π·16² = 256π

The area of the inscribed circle is 256π.

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5. Area of Circumscribed circle

The radius of the circumscribed circle is found in part 1 as 32. So the circle area is ...

  A = πr² = π·32² = 1024π

The area of the circumscribed circle is 1024π.

correct answer:

a + bi

step-by-step explanation:

1. practice, practice & more practice

2. review errors

3. master the key concepts

do not try to memorise the processes.

4. understand your doubts.

5. create a distraction free study environment

6. create a mathematical dictionary

7. apply maths to real world problems.