Math 9 Area of Parallelograms Lesson 19

Math 9 Area of Parallelograms Lesson 19

Journeys Page 197

Name SOLUTIONS

1.  Find the area.

A = Lw
= (4)(15)
= 60 cm2 / A = bh
= (2.1)(1.2)
= 2.52 m2 / A = bh
= (1.8)(0.83)
= 1.494 m2 / A = bh
= (10.5)(3.1)
= 32.55 cm2

2.  Sketch the rectangle. Then find the area.

a) base 14.1 m, height 5.25 m b) base 13.8 m, height 910 cm

c) base 45.1 cm, height 215 mm d) base x, height (x – 1)

A = LW
= (14.1)(5.25)
= 74.03 m / A = LW
= (13.8)(9.1)
= 125.58 m / A = LW
= (45.1)(21.5)
= 969.65 cm / A = LW
= (x)(x – 1)
= x2 - x

3.  Sketch the parallelogram. Then find the area.

a) base 12.1 m, height 11.9 m b) base 1.2m, height 53 cm

c) base x, height (x + 1) d) base (y + 2), height (y – 1)

A = bh
= (12.1)(11.9)
= 143.99 m / A = bh
= (1.2)(0.53)
= 0.636 m / A = bh
= (x)(x + 1)
= x2 + x / A = bh
= (y + 2)(y – 1)
= y2 + 2y – y – 2
= y2 + y - 2

4.  Betty plans to cover the top of her desk with plastic laminate. The laminate can be bought for $12.50/m2. Find the cost of covering the top of the desk.

5.  Find the area.

A = lw A = lw
= (2)(3) = (5)(6)
= 6 = 30
Total Area = Small Rec. + Large Rec.
= 6 + 30
= 36 m2 / A = lw A = lw A = lw
= (1)(0.35) = (1.5)(2) = (1.25)(0.75)
= 0.35 = 3 = 0.9375
Total Area = Rec. 1 + Rec. 2 + Rec. 3
= 0.35 + 3 + 0.9375
= 4.2875 m2
A = lw A = lw
= (x + 3)(x) = (3)(x)
= x2 + 3x = 3x
Total Area = Rec.1 + Rec. 2
= (x2 + 3x) + (3x)
= x2 + 6x / A = bh A = lw
= (x + 5)(x) = (x + 4)(x)
= x2 + 5x = x2 + 4x
Total Area = Parallelogram + Rec.
= (x2 + 5x) + (x2 + 4x)
= 2x2 + 9x

6.  a) How much grass seed is needed to cover the lawn area? 1.5 kg of grass seed covers 10.0 m2.

b) One bag of fertilizer covers 300 m2. How many bags of fertilizer are needed?

Walkway = lw House = lw Big Rec. = lw
= (9)(4) = (15)(12) = (30)(35)
= 36 = 180 = 1050
Total grass area = Big Rec. – Walkway – House
= 1050 – 36 – 180
= 834 m2
Grass Seed = 1.5 x 83.4 = 125.1 kg. / Fertilizer =
= 2.78 m
You need 3 bags of fertilizer.

7.  A section of a city street, 225 m long and 22 m wide, is to be resurfaced and curbs put in. Curbing costs $3.04/m and paving $14.27/m2. Find the total cost of the work.

Paving Area = lw
= (225)(22)
= 4950 m2
Cost = 4950 x $14.27 = $70 636.50 / Cost of Curbing = 225 x 2 x $3.04
= $1368

8.  Find the height of the rectangle.

a)  with area 24 cm2 and base 3.2 cm

b)  with area x2 – x – 12 and base x – 4.

h =
h =
h = 7.5 cm / h =
h =
h = x + 3