*These are regular polygons*
1.Find the area of a triangle with an apothem of 8 inches.
2.Find the area of a square with a radius of 12 inches.
3.Find the area of a pentagon with a hypotenuse of 10 inches.
1. To be speaking of an "apothem" of a triangle, the triangle must be equilateral.
The apothem is the distance from the centre (centroid) to a side, and the apothem must be 1/3 of the length of the median
so the median is 24 inches, which makes the height 24 inches.
then by knowing the ratio of sides of the 30-60-90 triangle, the side must be 48/√3
area = (1/2)(48/√3)(24) = 576/√3 square inches
2. We don't speak of a square having a radius.
Did you mean diameter?
if so let each side of square be x
x^2 + x^2 = 12^2
x = √98 =
area = x^2 = 98
3. Again, where does a hypotenuse come from in a pentagon?
Did you mean diagonal?
Find the internal angle. (you should get 108°)
From that you should be able to find all kinds of angles, depending on which lines you sketch.
a=8,r=16 , A=192*root Of 3.
1. To find the area of a triangle with an apothem of 8 inches, we need to know the length of the base. The apothem is the perpendicular distance from the center of the triangle to one of its sides.
2. It seems like there might be an error in the question. A square does not have a radius. It has sides of equal length. If we assume the side length of the square is 12 inches, we can find the area.
Area of a square = side length squared
So, the area of a square with a side length of 12 inches is 12 inches x 12 inches = 144 square inches.
3. To find the area of a pentagon with a hypotenuse of 10 inches, we need more information. The hypotenuse is usually associated with right-angled triangles, not regular pentagons. Please provide more details or verify the question.
To find the area of a regular polygon, you will need to use different formulas based on the given data. Let's go through each question step by step:
1. Find the area of a triangle with an apothem of 8 inches:
To solve this, we need more information. The apothem of a regular triangle is not enough to calculate its area. We also need either the length of one of the sides or the height. Once we have one of these values, we can use the formula: Area = (base × height) / 2.
2. Find the area of a square with a radius of 12 inches:
A square doesn't have a radius; it has sides of equal length. So, if the radius of a circle is given, it is unrelated to the area of a square. Therefore, we cannot find the area of a square based on the given information. However, if you are looking for the area of a circle given the radius of 12 inches, then the formula is Area of a Circle = π × radius^2.
3. Find the area of a pentagon with a hypotenuse of 10 inches:
It's important to note that "hypotenuse" is a term usually associated with right triangles, and not with regular pentagons. If you have a regular pentagon, you need either the length of one of the sides or the apothem to calculate its area. Once you have one of these values, you can use the formula: Area = (perimeter × apothem) / 2. The perimeter of a regular pentagon can be calculated by multiplying the length of one side by 5.