2-D Shapes and Areas
3-D Shapes and Formulas
Word Problems
Mixed Bag
Classify Shapes
100
What is the area formula for a triangle?
Answer: Area= 1/2 x base x height
A=1/2bh
100
What is the surface area of the cube?
Answer:
Surface Area = 6s2 --> 6(3)2 = 54 in2
100
True or False: Volume is always measured in units2.
Answer: FALSE --> Volume is measured in units3
100
What is the area of the shape below?
Answer: 9cm2
A = s2 --> 32 = 9 cm2
100
How many vertices does the shape below have?
Extra 100 points: Tell me what shape it creates.
Answer: 6 vertices
Vertices are where two 2-D faces connect and meet. They are the corners of 3-D shapes
Bonus: Triangular Prism
200
What is the area of the rectangle below?
Answer: 24cm2
Area = Length x width 8 x 3 = 24cm2
200
What is the volume of the rectangular prism?
Answer: 120in3
Volume = length x width x height
Volume = 4 x 10 x 3 = 120in3
200
A triangular banner has a base of 7mm and and height of 4mm. What is the area of the banner?
Answer: 14 mm2
Area = 1/2bh --> 1/2(7)(4)= 14mm2
200
How do I find surface area of a 3-D shape?
Answer: Find the area of each of the 2-D faces, and then add up add the areas.
200
What is this shape called?
Answer: A cube
It's a 3-D figure and all sides are the same!
300
What is the area of the shape below?
Answer: 72cm2
Area = base x height
Area = 6 x 12 = 72cm2
300
What is the surface area of the square pyramid?
Answer: 56m2
Surface Area = B + n(A)
B = 42 = 16 n = 4 triangles A= 1/2(5)(4) =10
16 +4 x 10 = 56m2
300
Devin wants to build a rectangular swimming pool with a length of 15.3ft and a width of 12.2ft. What is the area of the pool?
Answer: 186.66 ft2
Area =length x width = 15.3 x 12.2 = 186.66 ft2
300
How would you solve for the light blue portion of shape below? Bonus 100 points for solving the area of the blue portion?
Explain yourself in at least 3 steps.
Answer:
1) Find Area of Larger Rectangle: 15 x 10 = 150
2) Find Area of Smaller Rectangle: 9 x 6 = 54
3) Subtract the two to get the area of the blue:
150-54 = 96cm2
300
What is the name of the shape below?
Answer: Triangular Pyramid
The base is a triangle so it's a Triangular
All outside sides are triangles so it's a pyramid.
400
What is the area of the shape below?
Answer: 39m2
Area of a kite = 1/2x d1 x d2
d1 = 13m d2= 6 1/2 x 6 x 13 = 39m2
400
What is the surface area of the triangular prism below?
Answer: 144 in2
Surface Area: Add up all the areas of the faces (5 faces)
2 Triangles: 1/2(3)(4) = 6 x 2 = 12
1 bottom rectangle: 3 x 11 = 33
1 side rectangle: 4 x 11 = 44
1 side rectangle: 5 x 11 = 55
12 + 33 + 44 + 55 = 144 cm2
400
A play rug is shaped like a trapezoid. The width of the trapezoid is 5ft. The short base of the rug is the same as it width and the long base is 11ft. What is the area of the play rug?
Answer: 40ft2
Area = 1/2 x height x (base1 + base2)
1/2 x 5 x (5+11) = 40ft2
400
What is the volume of the rectangular prism?
Answer: 56cm3
Volume= length x width x height
7x2x4= 56cm3
400
How many edges does this shape have?
Bonus (100 points): How many vertices does it have?
Answer: 6 edges
The edges are the straight sides of a shape when two faces meet.
Bonus: 4 vertices (corners of the shape)
500
What is the area of the shape below?
Answer: 28 units2
Area = 1/2 x height x (base1+base2)
Area =1/2 x 4 x (6+8) = 28 units2
500
Find the surface area of the 3-D composite shape.
Answer: 144in2
9 Faces
1 square Area: 42 = 16
4 rectangles Area = 5 x 4 20 x 4 = 80
4 triangles Area: 1/2 x 4 x 6 = 12 x 4 =48
16 +80 + 48 = 144in2
500
A fish tank has a height of 3ft, width of 2 1/2 ft and a length of 5 1/4 ft. What is the volume of the fish tank?
Answer: 39 3/8 ft3
Volume = length x width x height
5 1/4 = 21/4 2 1/2 = 5/2 3= 3/1
21/4 x 5/2 x 3/1 = 315/8 = 39 3/8 ft3
500
What is the area of the composite shape?
Answer: 51.5ft2
Area of triangle: 1/2 x 3 x 2= 3ft2
Area of Triangle: 1/2 x 3 x 3 = 4.5ft2
Area of rectangle: 11 x 4 = 44ft2
Area = 3ft2+44ft2 + 4.5ft2= 51.5ft2
500
How many faces does this shape have?
Bonus 100 points: How would I find the surface area of the shape?
Answer: 9 faces
Four on top (triangles)
Four in the middle (rectangles)
One rectangle on the bottom
Bonus: Find the area of each of the faces and add them together!