Question

base, height, area
a. determine the base, height, and area of each shape.
b. discuss: what patterns do you notice?
shape\tbase (units)\theight (units)\tarea (sq. units)
i
j
k
l
m
n

Explanation:

Step1: Identify base and height of shape I

Count grid - squares. Base = 4 units, height = 2 units.

Step2: Calculate area of shape I

Use area formula for triangle $A=\frac{1}{2}\times base\times height$. So $A=\frac{1}{2}\times4\times2 = 4$ square units.

Step3: Identify base and height of shape J

Base = 4 units, height = 2 units.

Step4: Calculate area of shape J

Use area formula for parallelogram $A = base\times height$. So $A=4\times2 = 8$ square units.

Step5: Identify base and height of shape K

Base = 4 units, height = 2 units.

Step6: Calculate area of shape K

Use area formula for parallelogram $A = base\times height$. So $A=4\times2 = 8$ square units.

Step7: Identify base and height of shape L

Base = 3 units, height = 4 units.

Step8: Calculate area of shape L

Use area formula for parallelogram $A = base\times height$. So $A=3\times4 = 12$ square units.

Step9: Identify base and height of shape M

Base = 4 units, height = 3 units.

Step10: Calculate area of shape M

Use area formula for parallelogram $A = base\times height$. So $A=4\times3 = 12$ square units.

Step11: Identify base and height of shape N

Base = 5 units, height = 3 units.

Step12: Calculate area of shape N

Use area formula for parallelogram $A = base\times height$. So $A=5\times3 = 15$ square units.

Shape	Base (units)	Height (units)	Area (sq. units)
J	4	2	8
K	4	2	8
L	3	4	12
M	4	3	12
N	5	3	15

Answer:

Shape	Base (units)	Height (units)	Area (sq. units)
J	4	2	8
K	4	2	8
L	3	4	12
M	4	3	12
N	5	3	15

For part b:

• Patterns noticed: For parallelograms, when the base and height values are swapped (e.g., shape L with base 3 and height 4 and shape M with base 4 and height 3), the areas are the same. Also, the area of the triangle (shape I) with the same base - height pair as a parallelogram (shape J) is half of the parallelogram's area.