2D Geometry

Question 1

How do you calculate the area of a trapezoid?

Answer 1

Area equals base 1 + base 2 times 0.5 height.

Question 2

How do you calculate the area of a triangle?

Answer 2

Area equals 0.5 base times height.

Question 3

Explain circumference.

Answer 3

Circumference is the diameter times pi, or 3.14

Question 4

Explain how to order side lengths/angles.

Answer 4

The longest side length is the opposite of the longest angle.
The shortest side length is the opposite of the shortest angle.

Question 5

Explain the Triangle Inequality Theorem.

Answer 5

The Triangle Inequality Theorem is the theory that if sides x and y are less than or equal to z, the triangle is degenerate. If sides x and y equal more than z, the triangle is, well, a triangle.

Question 6

Explain how to find the area of a circle.

Answer 6

The area of a circle is found by multiply pi, or 3.14, by the radius of the circle, squared.

Question 7

Explain why 4, 5, 9, as side lengths, are able to make/not make a triangle.

Answer 7

4, 5, 9 as side lengths are not able to make a triangle because since 4+5 equals 9, the triangle would be degenerate, and would just be a line segment.

Question 8

Find the area of a decahedron with a apothem of 6 and a base of 20.

Answer 8

The answer should be 600 units, since 6 x 20 equals 120, and you divide by 2, which is 60, and multiply by 10.

Question 9

Find the area of a triangle where the height is 5 and the base is 12.

Answer 9

The area should be 30, since 5 x 12 equals 60, and is then divided by 2.

Question 10

Find the area of a parallelogram with a height of 10 and a base of 6.

Answer 10

The area should be 60.

Question 11

Find the area of a circle with the diameter of 40.

Answer 11

The area of the circle is 1,256 units.

Question 12

Find the circumference of a circle with an area of 314 units and a diameter of 20.

Answer 12

The circumference should be 62.8

Question 13

Find the circumference and area of a circle with the diameter of 20 meters.

Answer 13

C= 62.8
A= 314

Question 14

Determine the area of a trapezoid with a height of 4, and the bases the length of 5 and 10.

Answer 14

The area is 30 units.

Question 15

Determine the area of a trapezoid with a height of 40 meters, and the bases being a length of 20 and 50 meters.

Answer 15

The area is 1,400 meters.

Question 16

Explain why the side lengths of 13, 15, and 19, are able/unable to make a triangle.

Answer 16

The side lengths of 13, 15, and 19 are able to make a triangle because 13 + 15 equals 28, and 28 is more than 19, thus telling us that it is able to make a real triangle.