To solve, we will need to find the area of the wall. We can do this by finding the areas of each section and adding them together. Break the area into a rectange and two triangles.

The area of the rectangle will be equal to the base times the height. The area of each triangle will be one half its given base times its height.

For the rectangle, the base is 12 and the height is 4 (both given in the figure).

The triangle to the right has a given base of 6, but we need to solve for its height. The height will be equal to the difference between the total height (6) and the height of the rectangle (4).

We now have the base and height of the triangle to the right, allowing us to calculate its area.

Now we need to solve the triangle to the left. We solved for its height (2), but we still need to solve for its base. The total base of the rectangle is 12. Subtract the base of the right-side triangle (6) and the small segment at the top of the rectangle (3) from this total length to solve for the base of the left triangle.

The left-side triangle has a base of 3 and a height of 2, allowing us to calculate its area.

Add together the two triangles and the rectangle to find the total area.

We know that each bucket of paint will cover 5 square units, and we have 57 square units total. Divide to find how many buckets are required.

We will need 11 full buckets and part of a twelfth bucket to cover the wall, meaning that we will need 12 buckets total.

First, find the area of the circle.

Next, find the length of 1 side of the square using the Pythagorean Theorem. Two radii from the center of the circle to adjacent corners of the square will create a right angle at the center of the circle. The radii will be the legs of the triangle and the side of the square will be the hypotenuse.

Find the area of the square.

Subtract the area of the square from the area of the circle.

 is both one side of Square  and the hypotenuse of ;  its hypotenuse can be calculated from the lengths of the legs using the Pythagorean Theorem:

Polygon  is the composite of  and Square , so its area is the sum of those of the two figures. 

The area of  is half the product of its legs:

The area of  Square  is the square of the length of a side:

Add the areas:

This is the area of the polygon.

The area of  , the shaded region in question, is that of the rectangle minus those of  and . We look at both.

The answer is independent of the sidelengths of the rectangle, so to ease calculations - this will become more apparent later - we will arbitrarily assign to the rectangle the dimensions

and, subsequently,

and, since  is the midpoint of ,

.

The area of Rectangle  is equal to .

 Since , and ,

 and 

The area of  is equal to .

The area of  is equal to 

The area of the shaded region is therefore , which is

 of the rectangle.

To determine the measure of the angles of a regular polygon use:

Angle = (n – 2) x 180° / n

Thus, (n – 2) x 180° / n = 140°

180° n - 360° = 140° n

40° n = 360°

n = 360° / 40° = 9

The formula for of interior angles based on a polygon with a number of side n is:

Each Interior  Angle = (n-2)*180/n

= (7-2)*180/7 = 128.57 degrees

This question is very misleading, because while each answer COULD be true, none of them MUST be true. Between angle A and C, onne of the angles could be very small (0.001 degrees) and the other one could be very large. For instance, if A = 89.9999 and C = 0.0001, AC = 0.009. On the other hand, the two angles could be very siimilar. If B = 90 and D = 90 then BD = 8100 and BD > AC. If we use these same values we disprove AD = BC as 8100 ≠ .009. Finally, if B is a very small value, then B/C will be very small and smaller than A/D.

If angle A is one of the base angles, then the other base angle must measure 50 degrees. Since 50 + 50 + x = 180 means x = 80, the vertex angle must measure 80 degrees.

If angle A is the vertex angle, the two base angles must be equal. Since 50 + x + x = 180 means x = 65, the two base angles must measure 65 degrees.

The only number given that is not possible is 95 degrees.

Since the three angles of a triangle sum to 180, we know that 70 + x + y = 180. Subtract 70 from both sides and see that x + y = 110. Subtract x from both sides and see that y = 110 – x.

The sum of the interior angles, in degrees, of a regular polygon is given by the formula 180(n – 2), where n is the number of sides. The problem concerns a polygon with twelve sides, so we will let n = 12. The sum of the interior angles in this polygon would be 180(12 – 2) = 180(10) = 1800.

Because the polygon is regular (meaning its sides are all congruent), all of the angles have the same measure. Thus, if we divide the sum of the measures of the angles by the number of sides, we will have the measure of each interior angle. In short, we need to divide 1800 by 12, which gives us 150.

The answer is 150.