Geometry Answers

1. The radius of a regular decagon is 6m. What is the length of its apothem?
2. The area of a triangle with sides of length 10 in. and 17 in. and an included angle of 113° is equal to the area of a regular heptagon. Determine the length of each side of the heptagon.
3. Determine the area of the waste material in cutting out the largest circle (diameter is 23 cm) from a regular decagon.

1. The angle of a sector is 300 and the radius is 15 cm. Find its area and perimeter.
2. Obtain the area and perimeter of the segment of a circle whose radius is 11cm and central
angle of 75°?
3. The section of a rocket ship toy consists of a semicircle, a rectangle, and a triangle
as shown at the right. The altitude of a rectangle is three times the radius of the
semicircle, the altitude of the triangle is twice the same radius and the area of the
triangle is 20 sq. ft. Find the area of the section.

If DB bisects ADC m<1=(3x+4), and m<2=(5x-2) find x

1. Find the height of a parallelogram with 10 sides and 20 inches long, and an included angle of 35 degrees. Also, calculate the area of the figure.
2. A certain city block is in the form of a parallelogram. Two of its sides measures 32 ft and 41 ft. If the area of the land in the block is 656 ft^2, what is the length of its longer diagonal?
3. The area of an isosceles trapezoid is 246 m^2. If the height and the length of one of its congruent sides measures 6 meters and 10 meters, respectively, find the length of the two bases.

1. A rhombus has diagonals of 32 and 20 inches. Find the area and the angle opposite the longer diagonal.
2. If the diagonal length of a square is tripled, how much is the increase in the perimeter of that square?
3. The area of the rhombus is 156 m^2. If it's shorter diagonal is 13 meters, find the length of the longer diagonal.
4. The altitude BE of a parallelogram ABCD divides the side AD into segments in the ratio 1 is to 3. Find the area of the parallelogram if the length of its shorter side is 14 cm, and one of its interior angle measures 60 degrees.
5. The vertical end of a trough, which is in the form of a trapezoid, has the following dimensions: width at the top is 1.65 meters, width at the bottom is 1.15 meters, and depth is 1.35 meters. Find the area of this section of the trough.

1. An isosceles trapezoid has an area of 40 m^2 and an altitude of 2 meters. Its two bases have a ratio of 2 is to 3. What are the lengths of the bases and one diagonal of the trapezoid?
2. A piece of wire of length 52 meters is cut into two parts. Each part is then bent to form a square. It is found that the combined area of the two squares is 109 m^2. Find the measure of the sides of the two squares.

1. Find the height of a parallelogram with 10 sides and 20 inches long, and an included angle of 35 degrees. Also, calculate the area of the figure.
2. A certain city block is in the form of a parallelogram. Two of its sides measures 32 ft and 41 ft. If the area of the land in the block is 656 ft^2, what is the length of its longer diagonal?
3. The area of an isosceles trapezoid is 246 m^2. If the height and the length of one of its congruent sides measures 6m and 10m, respectively, find the length of the two bases.

Determine the range of values of θ ∈ [0, 2 π] for which the point (cos θ, sin θ) lies inside the triangle formed by the lines x + y = 2 ; x − y = 1 & 6x + 2y − 10 = 0.

Determine all values of α for which the point (α, α²) lies inside the triangle formed by the lines 2x + 3y − 1 = 0 ; x + 2y − 3 = 0 ; 5x − 6y − 1 = 0.

Consider the family of lines, 5x + 3y − 2 + K1 (3x − y − 4) = 0 and x − y + 1 + K2(2x − y − 2)=0. Find the equation of the line belonging to both the families without determining their vertices.