Week 2- Idea Lab( discussion)
1. Give a formal definition for the following figures and the formula for finding the area of each. Include
a picture of each with the definition and what object in the real world might have inspired the shape.
Also, give an example of finding the area of at least two your figures.
Triangle:
A closed 2-dimesional shape (polygon) that consist of 3 sides, 3 angles and 3 vertices.
Formula: A=1/2*Base*Height (A= 1/2*b*h)
Square:
A 2-dimensional shape with four equal sides of 90 degrees.
Formula: A=Side*side (A=s*s)
If the sides of a square are 7cm the formula translates to: A= (7cm)^2 or 7*7.
A=49.
Rectangle:
Convex polygon that has four right angles also known as a quadrilateral.
Formula: A= Length*width (A=L*W)
Circle:
A round shaped figure with no corners or edges.
Formula: A=pi*radius^2 (A=pi*r^2) (pi =3.14)
If the radius of this circle is 7cm, we plug and play the formula
A=Pi*r^2
A=(3.14)*7^2
49(3.14)
A=153.86cm^2
Answer a, b, & c below about right triangles
2. In a right triangle if angle A is 30°, what are the measures of the other two angles? Explain Why
, Using the Pythagorean Theorem, find the hypotenuse of a right triangle with sides measuring a = 3 and b
= 4. Show work.
Using the Pythagorean Theorem, find the length of the side of a right triangle with the hypotenuse = 10
and the other side measuring a = 6. Show all work.
a. In a right triangle, if angle A is 30°, what are the measures of the other two angles? Explain why.
In a right triangle, one angle is always 90°. If angle A=30∘A = 30°, the sum of the angles in a triangle is
180°. Therefore:
Angle C=180°−90°−30°=60°
Explanation: The sum of the angles in a triangle is always 180°, and one angle in a right triangle is 90°.
The remaining two angles must add up to 90°, so if one of them is 30°, the other must be 60∘
b. Using the Pythagorean Theorem, find the hypotenuse of a right triangle with sides a=3 and b=4 . Show
work.
The Pythagorean Theorem states:
C2=a2+b2
Substituting a=3 and b=4
C2=9+16
C2=25, C= √25
C= 5
Answer: The hypotenuse of the triangle is 5.
c. Using the Pythagorean Theorem, find the length of the side of a right triangle with the hypotenuse
c=10 and one side a=6 . Show all work.
The Pythagorean Theorem states:
C2=a2+b2
Rearranging to solve for b2
B2=c2−a2
Answer: Substituting c=10 and a=6
B2=102−62
Taking the square root of both sides:
1. Give a formal definition for the following figures and the formula for finding the area of each. Include
a picture of each with the definition and what object in the real world might have inspired the shape.
Also, give an example of finding the area of at least two your figures.
Triangle:
A closed 2-dimesional shape (polygon) that consist of 3 sides, 3 angles and 3 vertices.
Formula: A=1/2*Base*Height (A= 1/2*b*h)
Square:
A 2-dimensional shape with four equal sides of 90 degrees.
Formula: A=Side*side (A=s*s)
If the sides of a square are 7cm the formula translates to: A= (7cm)^2 or 7*7.
A=49.
Rectangle:
Convex polygon that has four right angles also known as a quadrilateral.
Formula: A= Length*width (A=L*W)
Circle:
A round shaped figure with no corners or edges.
Formula: A=pi*radius^2 (A=pi*r^2) (pi =3.14)
If the radius of this circle is 7cm, we plug and play the formula
A=Pi*r^2
A=(3.14)*7^2
49(3.14)
A=153.86cm^2
Answer a, b, & c below about right triangles
2. In a right triangle if angle A is 30°, what are the measures of the other two angles? Explain Why
, Using the Pythagorean Theorem, find the hypotenuse of a right triangle with sides measuring a = 3 and b
= 4. Show work.
Using the Pythagorean Theorem, find the length of the side of a right triangle with the hypotenuse = 10
and the other side measuring a = 6. Show all work.
a. In a right triangle, if angle A is 30°, what are the measures of the other two angles? Explain why.
In a right triangle, one angle is always 90°. If angle A=30∘A = 30°, the sum of the angles in a triangle is
180°. Therefore:
Angle C=180°−90°−30°=60°
Explanation: The sum of the angles in a triangle is always 180°, and one angle in a right triangle is 90°.
The remaining two angles must add up to 90°, so if one of them is 30°, the other must be 60∘
b. Using the Pythagorean Theorem, find the hypotenuse of a right triangle with sides a=3 and b=4 . Show
work.
The Pythagorean Theorem states:
C2=a2+b2
Substituting a=3 and b=4
C2=9+16
C2=25, C= √25
C= 5
Answer: The hypotenuse of the triangle is 5.
c. Using the Pythagorean Theorem, find the length of the side of a right triangle with the hypotenuse
c=10 and one side a=6 . Show all work.
The Pythagorean Theorem states:
C2=a2+b2
Rearranging to solve for b2
B2=c2−a2
Answer: Substituting c=10 and a=6
B2=102−62
Taking the square root of both sides:
