The perimeter of an equilateral triangle would be known, but the type of triangle is unknown in the problem statement.

The perimeter of a triangle requires three known sides.  Since only one side is given, we do not have enough information to determine the perimeter.

The answer is:  

To find the perimeter of a triangle, we will use the following formula:

where a, b, and c are the lengths of the sides of the triangle.

Now, given the triangle

we can see it has sides with lengths 10ft, 6ft, and 12ft. So, we can substitute. We get

To find the perimeter of a triangle, we will use the following formula:

where a, b, and c are the lengths of the sides of the triangle.

Now, given the triangle

we can see one side is 4ft. Because it is an equilateral triangle, all sides are equal. Therefore, all sides are 4ft. So, we can substitute. We get

To find the perimeter of an equilateral triangle, we will use the following formula:

where a is any side of the equilateral triangle. Because an equilateral triangle has 3 equal sides, we are able to use any side in the formula. 

Now, we know the base of the equilateral triangle is 13cm. So, we can substitute. We get

All three sides of an equilateral triangle are equal.

We will need to multiply the side length by three.

The answer is:  

No two of the sides are of equal length, making the triangle scalene.

To determine whether it is acute or obtuse, add the squares of the lesser lengths, and compare the sum to the square of the greatest length:

The sum of the squares of the lesser lengths exceeds the square of the greatest length, so the triangle is acute.

The correct response is that the triangle is scalene and acute. 

No two of the sides are of equal length, making the triangle scalene.

To determine whether it is acute or obtuse, add the squares of the lesser lengths, and compare the sum to the square of the greatest length:

The square of the greatest length exceeds the sum of the squares of the lesser lengths, so the triangle is obtuse.

The correct response is that the triangle is scalene and obtuse.

The perimeter of any figure is the sum of all the lengths of that figure.

An equilateral triangle is a triangle where the length of all three sides is the same length. So, all sides of the triangle have a length of cm. 

So, the perimeter is , or cm.

First we need to know that in an isosceles triangle, 2 sides are equal in size so we know that since one side is 8cm, the other side is also 8cm.

We are also given information that the base is half the length of the size, and half of 8 is 4, so our base is 4cm.

The perimeter of any triangle is found when adding up all sides.

In this case we add up 

The answer is independent of the sidelengths of the rectangle, so to ease calculations, we will arbitrarily assign to Square  sidelength 4 inches. 

The shaded region can be divided by a perpendicular segment from  to , then another from  to that segment, as follows:

By the fact that rectangles have opposite sides that are congruent, and by the fact that  is the midpoint of and  is the midpoint of , the shaded region is a composite of:

Square , which has sides of length 2 and therefore area ;

Right triangle , which has two legs of length 2 and, thus, area ; and,

Right triangle , which has legs of length 4 and 2 and, thus, area .

The area of the shaded region is therefore .

Square  has area , so the shaded region is

of the square.