Reasoning to find Area
What is the formula for the area of a rectangle?
Area=length x width
What is the formula for the area of a parallelogram?
Area=base×height
What is the formula for the area of a triangle?
1/2 base x height
What does surface area mean?
The total area of all the faces of a 3D figure.
What 3D shape is made if you fold a net of 6 equal squares?
A cube.
A rectangle has an area of 48 and a base of 6. What is the height?
8
True or False: The slanted side of a parallelogram is always the height.
False
A triangle has a base of 10 and height of 6. What is its area?
30
How many faces does a cube have?
6
What shape is made by folding a net of rectangles and two triangles?
Triangular prism
A triangle has the same area as a rectangle with base 12 and height 4. What is the area of the triangle?
48
A parallelogram has a base of 12 and height of 5. What is its area?
60
A triangle’s area is 24 and its base is 12. What is the height?
4
A cube has side length 3. What is its surface area?
54
A net is made of 4 rectangles and 2 squares. What 3D figure will it make?
A rectangular prism
A rectangle has an area of 36. Name one possible pair of side lengths.
Length = 4
Width = 9
Other answers possible.
A parallelogram has area 24 and base 6. What is the height?
A triangle has an area of 40. If the height is 8, what is the base?
10
A rectangular prism is 2 by 3 by 5. What is its surface area?
62
A net is made of 2 triangles and 3 rectangles. The triangles are right triangles. What figure does it make?
A triangular prism
A figure is made of a rectangle (5 by 8) and a triangle (base 5, height 4) attached to the top. What is its total area?
50
Draw or describe two different parallelograms with an area of 18 square units.
(Answers will vary, e.g., base 9 height 2, or base 6 height 3, etc.)
On a triangle, draw the height that corresponds to a given base.
Answers vary.
Polyhedron P is a cube with a corner removed and moved to the top. Polyhedron Q is a full cube. Which has more surface area?
Polyhedron P.
A triangular prism has 2 triangular bases and 3 rectangular faces. If each triangular base has an area of 12 cm² and the three rectangles have areas of 15 cm², 20 cm², and 20 cm², what is the total surface area of the prism?
79 cm²