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Q: What is the area of a 30-60-90 triangle with the smallest side being cm?

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You cannot. For a given area, an equilateral triangle will have the smallest perimeter but that perimeter can be increased - without limit - without increasing the area.

This is how you find the area of a regular pentagon: Break it into five isosceles triangles by drawing lines from the middle of it to each vertex. Then, draw a line connecting the middle to the midpoint of a side. You can call that line the apothem. The apothem should break up one of the triangles into two smaller congruent right triangles. You can know the degrees in the triangle by dividing the central angle of 360 by 10, (dividing it by 10 because your smallest triangle you're going to use is 1/10th of the whole pentagon) So now you know the unknown angle towards the top of the smallest triangle is 36, do the subtraction so the unknown angle towards the bottom is 54. Now trig it out! SOH-CAH-TOA shows that tan(54)=(a/s). A being the apothem and s being the side length of the smallest triangle, which is half a side length. Now that you know the lengths of the smallest triangle, find the area of that. That triangle is replicated 10 times in the pentagon, so multiply it by 10.

The dimensions given would not form a triangle. The sum of a triangles 2 smallest sides must be greater than the triangle's longest side.

It is base x height for the parallelogram. That is twice the area of a triangle which is: 1/2 base x height. (Base and height being the same for both cases).

Doubling the base of a triangle while keeping the height constant will double the area of the triangle. The area of a triangle is directly proportional to its base length, so increasing the base length by a factor of 2 will result in the area being multiplied by 2 as well.

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You cannot. For a given area, an equilateral triangle will have the smallest perimeter but that perimeter can be increased - without limit - without increasing the area.

This is how you find the area of a regular pentagon: Break it into five isosceles triangles by drawing lines from the middle of it to each vertex. Then, draw a line connecting the middle to the midpoint of a side. You can call that line the apothem. The apothem should break up one of the triangles into two smaller congruent right triangles. You can know the degrees in the triangle by dividing the central angle of 360 by 10, (dividing it by 10 because your smallest triangle you're going to use is 1/10th of the whole pentagon) So now you know the unknown angle towards the top of the smallest triangle is 36, do the subtraction so the unknown angle towards the bottom is 54. Now trig it out! SOH-CAH-TOA shows that tan(54)=(a/s). A being the apothem and s being the side length of the smallest triangle, which is half a side length. Now that you know the lengths of the smallest triangle, find the area of that. That triangle is replicated 10 times in the pentagon, so multiply it by 10.

I do believe you mean RIGHT triangle when you said perpendicular triangle. A right triangle has two legs and a hypotenuse. The area of a right triangle is 1/2 * (first leg) * (second leg) How do you determine which ones are the legs and which one is the hypotenuse? The hypotenuse is ALWAYS the largest number. So, choose the 2 smallest numbers.

The dimensions given would not form a triangle. The sum of a triangles 2 smallest sides must be greater than the triangle's longest side.

It is 5.196*r^2 square units.

It is base x height for the parallelogram. That is twice the area of a triangle which is: 1/2 base x height. (Base and height being the same for both cases).

Doubling the base of a triangle while keeping the height constant will double the area of the triangle. The area of a triangle is directly proportional to its base length, so increasing the base length by a factor of 2 will result in the area being multiplied by 2 as well.

The area of a triangle is one half base times height. In the case of a right triangle, the base is one leg and the height is the other leg. (The two legs being separated by the right angle.)

circle has the smallest area

Area of Equilateral Triangle A= S2 * (Root 3)/4, where A= Area of the triangle S= Side of the triangle.

The state with the smallest land area is Rhode Island

The area of triangle is : 24.0