Exercise 13.2

1. Find the area of each of the following parallelograms.

(2) PQRS is a parallelogram. PM is the height from P to SR and PN is the height from P to QR. If SR = 12 cm and PM = 7.6 cm.

(i) Find the area of the parallelogram PQRS

Area of parallelogram = ×

Base = SR = cm

Height = PM = cm

Area = × = cm²

(ii) Find PN, if QR = 8 cm

Area remains the same when using different base and height

Using base QR = cm and height PN

Area = QR × PN = × PN =

PN = ÷

PN = cm

(3) DF and BE are heights on sides AB and AD respectively in parallelogram ABCD. If area = 1470 cm², AB = 35 cm and AD = 49 cm, find the length of BE and DF.

Finding DF (height on side AB):

Area = base × height

Using base AB = cm and height DF

= × DF

DF = ÷

DF = cm

Finding BE (height on side AD):

Using base AD = cm and height BE

= × BE

BE = ÷

BE = cm

(4) The height of a parallelogram is one third of its base. If the area of the parallelogram is 192cm², find its height and base.

Let base = cm

Height = × base = cm

Area = base × height

= b ×

192 = /

b² = 192 × =

b = 576= cm

Base = cm

Height = ÷ 3 = cm

Height = cm

(5) In a parallelogram the base and height are in the ratio of 5:2. If the area of the parallelogram is 360 m², find its base and height.

Base : Height = :

Let base = and height =

Area = base × height

360 = ×

360 = k2

k2 = 360 ÷ =

k =36 =

Base = 5k = 5 × = m

Base = m

Height = 2k = 2 × = m

Height = m

(6) A square and a parallelogram have the same area. If a side of the square is 40m and the height of the parallelogram is 20m, find the base of the parallelogram.

Area of square = side × side = ×

Area of square = m²

Area of parallelogram = Area of square = m²

Area of parallelogram = base × height

= base ×

Base = ÷

Base = m