5th Grade - Area Of Triangles And Parallelograms

 
     
 
     
 
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5th
Shapes and Geometry
Area of Triangles and Parallelograms
Derive and use the formula for the area of a triangle and of a parallelogram by comparing it with the formula for the area of a rectangle (i.e., two of the same triangles make a parallelogram with twice the area; a parallelogram is compared with a rectang
Ability to calculate area of a parallelogram, triangle and rectangle. Ability to relate the area of a parallelogram to a triangle and rectangle.
 

Sample Problems

(1)

Find the area of the rectangle.


A=l x w

A= 9cm x 7cm

A=63 cm2 7cm




9cm


(2)

Find the area of the triangle


A= ½ base x height

A= ½ (9cm x 10cm) 9cm

A= ½ (90cm)

a=45cm2

10cm




(3)

Find the area of parallelograms

A=b x h

A= 10m x 5m

A= 50 m2


5m




10m







(4)

Find the area for the given shape.


A= l x w

A= 16in x 5in

A= 80 in2 16in





5in



(5)

Find the missing measurement for a parallelogram. (b=4 cm)


Base (b) =?

Height (h) =12in

Area (a) =20 cm2


Learning Tips

(1)

Math Vocabulary:

Angle: The shape formed by two rays (called sides of the angle) with the same endpoint (called the vertex of the angle). In geometry an angle can be defined by the vertex or by the rays and vertex

Perimeter: The distance around a figure

Area: number of square units need to cover a surface. (formula for area = length x width)

Parallelogram: a quadrilateral with parallel and congruent opposite sides.

Parallel lines: Lines that are always the same distance apart, they never cross.

Triangle: A polygon with three sides and three angles

Base: a side of a polygon

Height: the length of the perpendicular line segment from the vertex to the base of the triangle.

(2)

To find the area of a rectangle you need to use the formula (a= l x w).

Area of rectangle = length times width




2cm


A=l x w 9cm

A=9 x 2

A=18cm2



(3)

To find the area of a rectangle you need to use the formula (a= l x w).

To find the area of a square you need to use the formula (a=s x s )

Area of rectangle = length times width




2cm


A=l x w

A=6 x 2

A=12cm2 6cm


Area of Square:

A= side x side

A= s x s 7cm

A= 7cm x 7cm

A=49cm2

7cm






(4)

To find the area of a parallelogram, tell your child to use what they know about the area of a rectangle, and triangle.

The area of a parallelogram is equal to the area of a rectangle with the same base and height. (b x h)

Use a formula to find the area of a parallelogram. The area is equal to the area of a rectangle with the same base (length)and height ( width)( a= b x h)




base=10 cm height 3in


a= b x h

a= 6 in x 3 in

a= 18 in2 base = 6 in


(5)

Copy a parallelogram onto paper and cut it out. Then draw a right angle using a line segment. See example.


Step1: Example






Step 2: Cut this right triangle out and move it to the right side of parallelogram to form a rectangle


Example:



5cm



11cm


Step 3: Example: The rectangle has the same area as the parallelogram.

Area = 55cm2


Extra Help Problems

(1)

Find the area of a rectangle


A= 60cm2

4cm



15cm




(2)

Find the area of a rectangle



a=27 in2

3m


9m

(3)

Find the area of a rectangle


a= 24 cm2



2cm

12cm


(4)

Find the area of a rectangle


A= 25.55 in2

7.3 in


3.5in


(5)

Find the area of a rectangle



A= 181.5 cm2 11cm




16.5cm


(6)

Find the area of the triangle.

a = 10 cm2 4cm



5cm

(7)

Find the area of the triangle.


A=3 ½ yd


2 yd




3 ½ yd


(8)

Find the area of the triangle.


A=40 m2

5m



16m

(9)

Find the area of the triangle.


A=35 in2


5in



14in


(10)

Find the area of the triangle.

A= 38.5 yd2



7yd

11yd



(11)

Find the area of parallelograms

A= 32.86cm2



6.2cm







5.3cm



(12)

Find the area of parallelograms


A= 126 ft2

10.5ft




12ft

(13)

Find the area of parallelograms


A=88 cm2



8cm




11cm



(14)

Find the area of parallelograms


A=112.5 in2

5in




22.5in







(15)

Find the area of parallelograms

A= 25in2



5in




5in


(16)

Find the area for the given shape a=26.875 cm2




4.3cm




. 6.25cm


(17)

Find the area for the given shape. A= 45.5 ft2


7ft





13ft

(18)

Find the area for the given shape. A= 19.84 in2



3.2in





6.2in

(19)

Find the area for the given shape. A=108 cm2




12cm



9cm


(20)

Find the area for the given shape. A=48 in2




6in





8in

(21)

Find the missing measurement for the rectangle. l=3.2m


L=? m

W= 4m

A= 12.8 m2


(22)

Find the missing measurement for the parallelogram. H=12in


B=3in

H=? in

A=36 in2



(23)

Find the missing measurement for the parallelogram. Base=11ft

B=? ft

H= 9 ft

A= 99 ft2




(24)

Find the missing measurement for the triangle. B=5ft


B=?ft

H=6ft

A=15 ft2




(25)

Find the missing measurement for the triangle. H=4.7cm


b= 2.6 cm

h=? cm

a= 6.11 cm2



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