# 5th Grade - Area Of Triangles And Parallelograms

 Grade Level: 5th Skill: Shapes and Geometry Topic: Area of Triangles and Parallelograms Goal: 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 Skill Description: 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