Pythagorean Theorem Theory
Pythagorean Theorem Problems
Area
Volume
Surface Area
100
What type of triangles are used in the Pythagorean Theorem?
Right triangles
100
Find the third side.
a = 23.6
b = 55.5, c = 60.3
100
What is the definition of area?
the space inside of a 2D shape
100
What is the defintion of volume?
The amount that fits inside of a 3D object.
100
What is the defintion of surface area?
sum of all of the areas of a 3D shape
200
What is the letter that is always across from the right angle?
C
200
The two legs of the right triangle are 80cm and 30 cm. What is the length of the third side?
85.4 cm
200
What is the area formula for a circle?
A = pi x r2
200
What is the basic formula for Volume of a prism?
V = AREA OF THE BASE X HEIGHT
200
A rectangular prism is 4.3 m long, 2.3 m wide and 8.1 m high. What is the surface area?
SA = 126.7 m2
300
How do you solve for the letter a?
a2 = c2 - b2 then take the square root.
300
The bottom of a ladder must be placed 3 feet from a wall. The ladder is 12 feet long. How far above the ground does the ladder touch the wall?
11.6m above the ground.
300
What is the area formula for a triangle?
A =bh/2
300
What is volume of a rectangular prism that is 3 ft long by 4 ft wide by 8 ft tall?
V = 3 x 4 x 8 = 96 ft3
300
What is the surface area for this cylinder?
r = 5.3 in h = 6.7 in
SA = 399.6 in2
400
What is the formula for finding b?
b2 = c2 - a2 then take the square root
400
Daniel rides his bicycle 21 km west and then 18 km north. How far is he from his starting point?
c = 27.7 km
400
What is the area of this triangle?
b = 8, h = 7
A = 28 cm2
400
The diameter of a cylindrical tank is 9 feet and the height is 25 feet. How much water can the tank hold if filled to the top?
V = 1590.4 ft3
400
What is the surface area for this triangular prism?
b = 4 cm, h = 3 cm, slant height = 5 cm other slant height 8 cm, height of prism 13 cm.
SA = 233 cm2
500
What is the formula for finding c?
c2 = a2 + b2 then take the square root.
500
John is trying to determine the length of the staircase he will need for a deck that is 12 feet high. He wants to start the stairs 21 feet from the deck. What is the length of the staircase?
24.2 feet long.
500
What is the area of this circle?
r = 6.2 cm
A = 120.8 cm2
500
What is the volume of the Triangular prism?
b = 5 m, h(of triangle) = 7 m and h(of prism) = 12 m
V = 210 m3
500
You are making a round cake with two layers. The bottom layer has a diameter of 9 in. and the top layer has a diameter of 7 in. Both layers are 6 in. high. How much fondant is needed to cover the cake?
SA = 365.2 in2