Parallelograms
What is the formula to find the area of a parallelogram?
A = b x h
What is the formula to find the area of a triangle?
A = b x h ÷ 2
How do we find the area of a composite shape?
Split the shape into rectangles and triangles, find each area, and add each area up!
What is the formula to find the volume of a rectangular prism?
What do I ALWAYS need after I find the answer to my word problem?
A sentence!
Fill in the blank:
Parallelograms are made of two __________ _________.
congruent triangles
Why do we have to divide by 2 when we find the area of a triangle?
We have to divide by 2 when finding the area of a triangle because one triangle is half of a rectangle or parallelogram, so the area is also half.
A shape is made of:
• Rectangle: 6 m × 4 m
• Triangle: base 6 m, height 3 m
What is the total area?
Rectangle: A = b x h = 6 x 4 = 24m2
Triangle: A = b x h ÷ 2 = 6 x 3 ÷ 2 = 9m2
Add them: 24 + 9 = 33m2
What should my units ALWAYS be when finding the volume?
Units are always cubed!
-mm3
-cm3
-m3
A triangular sail on a boat has a base of 8 m and a height of 5 m. What is the area of the sail?
A = b x h ÷ 2
A = 8 x 5 ÷ 2
A = 20m2
The area of the sail is 20m2.
A parallelogram has a base of 6m and a height of 3m. What is the area?
A = b x h
A = 6 x 3
A = 18m2
If a triangle has a base of 2mm and a height of 10mm, what is the area of the triangle?
A = b x h ÷ 2
A = 2 x 10 ÷ 2
A = 20 ÷ 2
A = 10mm2
A student added base × height for BOTH parts of a composite shape, EVEN for the triangle.
What mistake did they make?
For the triangle, they forgot to divide the area by 2. They would have to do:
A = b x h for the rectangle and
A = b x h ÷ 2 for the triangle and add them together
Rectangular prism dimensions:
Length = 6 cm, Width = 4 cm, Height = 2 cm
What is the volume?
V = l x w x h
V = 6 x 4 x 2
V = 48cm3
A garden bed is shaped like a parallelogram with a base of 11 m and a height of 7 m. What is the area of the garden bed?
A = b x h
A = 11 x 7
A = 77m2
The area of the garden bed is 77m2.
A parallelogram has a height of 8cm and a base of 4cm. What is the area?
A = b x h
A = 4 x 8
A = 32cm2
A triangle has a base of 6m and a height of 7m. What is the area of the triangle?
A = b x h ÷ 2
A = 6 x 7 ÷ 2
A = 42 ÷ 2
A = 21m2
A composite shape is made of:
• Rectangle: 8 m × 5 m
• Triangle 1: base 8 m, height 4 m
• Triangle 2: base 5 m, height 2 m
What is the total area?
Rectangle: A = b x h = 8 x 5 = 40m2
Triangle 1: A = b x h ÷ 2 = 8 x 4 ÷ 2 = 16m2
Triangle 2: A = b x h ÷ 2 = 5 x 2 ÷ 2 = 5m2
Total area = 40m2 + 16m2 + 5m2 = 61m2
A rectangular prism has dimensions:
Length = 4 cm, Width = 3 cm, Height = 4 cm
A student calculates:
V = l x w x h = 4 × 3 × 4 = 48 and writes the answer as 48m².
What is wrong with the student’s answer?
The units are cm3 and NOT m2
A cereal box measures a length of 4cm, a width of 2cm and a height of 10cm. What is the volume of the cereal box?
V = l x w x h
V = 4 x 2 x 10
V = 80cm3
The area of the cereal box is 80cm3.
A parallelogram has an area of 35m2 and a base of 5m. What is the height?
h = A ÷ b
h = 35 ÷ 5
h = 7m
A triangle has a height of 11cm and a base of 8cm. What is the area of the triangle?
A = b x h ÷ 2
A = 6 x 11 ÷ 2
A = 88 ÷ 2
A = 44cm2
The TOTAL area of a shape is 50 cm².
One rectangle part is 8 cm × 5 cm, but the area of the triangle is unknown.
What is the area of the triangular part?
Rectangle: A = b x h = 8 x 5 = 40cm2
Total are: 50cm2 = 40cm2 + triangle area
Triangle area = 50cm2 - 40cm2
Triangle area = 10cm2
Volume = 24cm³
Length = 3cm
Width = 2cm
What is the height?
V = l x w x h
24 = 3 x 2 x h
24 = 6 x h
24 ÷ 6 = h
4 = h
The height is 4cm
A community garden is shaped like a rectangle.
The garden is 10m long and 6m wide.
Soil is sold in bags, and each bag covers 5m² of garden space.
How many bags of soil are needed to completely fill the garden?
Area of garden = b x h = 10 x 6 = 60m2
Number of bags = 60 ÷ 5 = 12
It will take 12 bags of soil to fill the garden.