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Find the volume of a tetrahedron and an octahedron.

I need help writing a proof of the formulas of the volumes of two regular polyhedra (Platonic solids): (1) a tetrahedron and (2) an octahedron. I then have to use those formulas to find the volumes given a side length of 1.

Lengths and Angles of a Triangle

Solve the triangle, round lengths to the nearest tenth and angle measures to the nearest degree. Please show work and see attachment.

Saccheri quadrilaterals; Lambert quadrilaterals

Draw a diagram of a Saccheri quadrilateral ABDC, where (a) A and B are a pair of consecutive vertices (b) sides AD and BC are a pair of opposite sides (c) angles A and B are right angles (d) sides AD and BC are congruent. Then let M be the midpoint of AB, and drop a perpendicular from M to CD with foot N. Once

Similar Triangles Measured

Surveying: Surveyors sometimes use similar triangles to measure inaccessible distances. A surveyor could find distance AB by setting up similar triangles ABC and EDC. Assuming all lengths may be directly measured to set up a proportion and solve for AB. 17. How does the surveyor make ABC similar to EDC? 18. Set up a prop

Calculating Volume

6. What is the volume of a regular square pyramid which has a total area of 360 if the square base is 10 on a side. 9. How long is the edge of a cube whose total area is numerically equal to it's volume? 15. A cube has a cylinder inscribed inside of it. That cylinder has a sphere inscribed inside of it. What is the rati

Geometry Problems

Geometry has many practical applications in everyday life. Estimating heights of objects, finding distances, and calculating areas and volumes are commonplace. One of the most fundamental theorems in geometry, the Pythagorean Theorem, allows us to make many of these calculations. The Pythagorean Theorem states that the square of

Finding Length of the Side of a Triangle

Given a=41degrees, B=101degrees, and a=30.1, approximate the length of side b in a triangle ABC. Given a=100degrees, B=30degrees, and c=110.3, approximate the length of side b in a triangle ABC.

Geometry : Triangle in a Cone

In the diagram attached, I have to show that: curly r-bar = sqrt(h^2 + curly-r squared - sqrt(2).h.curly-r). So far, I've only been able to come up with the obvious fact that: curly - r^2 = sqrt(h^2+h^2) = sqrt(2).h

Geometry : Medians of Triangle Proof

O is the intersection point of the medians of a triangle ABC. The medians are AD, BE, CF. what is the ratio of the area of triangle EOC to triangle ABC?

Geometry : Right Triangle Inscribed in a Circle

Using the diagram attached: 11. What is the measure of arc AC? 12. If ABC is a 30-60-90 triangle, with angle ACB at 30 degrees, and line segment AC is the diameter of the circle, then if the length of line segment AB is 4, what is the radius of the circle? 13. Working with the information from 12 from here to #16, what is

Arcs and chords of a circle.

Using the diagram at right: 1. If the diameter of circle M is 20, and the length of line segment DF is 12, what is the length of segment MJ? 2. If the measure of arc BFE is 80 degrees, then what is the measure of angle BME? 3. If there were an imaginary angle ACB, what would the measure of that angle be? (Hint: Remember that

Solutions to problems in geometry

See attached file for full problem description. 1. Use the figure below to find the following: 2. a) Find the complementary angle of 26 b) DEF and GHI are supplementary angles and GHI is fourteen times as large as DEF. Determine the measure of each angle

Solving for Geometry Word Problems

a. A certain wheel has a diameter of 98 inches. If that wheel travels for 108 revolutions, then. Questions: How many years has it gone? (use 22/7 for pi) b. A regular hexagon and an equilateral triangle are equal in area. The perimeter of the triangle is 36. Question: How long is one side of the hexagon? c. The base of

Area and Perimeter of Triangles

28. Find the area and perimeter of an equilateral triangle whose altitude measures 6 cm. 29. If the area of an equilateral triangle is 100 sq cm, find the length of a side.

High School Geometry Problems

Please see the attached file for the fully formatted problems. Given: <D and <C are right angles (triangle APR) = (triangle BQT) Prove: (triangle ADF) = (triangle BCE)

Geometry: Congruent Triangles

Given: The triangle ABC is an equilateral triangle and the angle 1 = the angle 2 = the angle 3. Prove: The triangle AFC, the triangle CEB and the triangle BDA are all congruent.

Area of an isosceles triangle and volume of a prism.

If I have a right prism with the prism height being 8 and the prism base being an isosceles triangle with a base of 3 (sides of 6) what is the lateral area and the volume of the prism, also what is the triangle's height by using the Pythagorean theorem?

Find the area covered by the chemical retardant.

1) In mountain communities, helicopters drop chemical retardants over areas which approximate the shape of an isosceles triangle having a vertex angle of 38 degrees. The angle is included by two sides, each measuring 20 ft. Find the area covered by the chemical retardant. 2) The chemical retardants are freight shipped from