Question

The two sides of the parallelogram ABCD are 6 cm and 4 cm. The height
corresponding to the base CD is 3 cm (Fig 11.19). Find the area of parallelogram and the height corresponding to the to the base of ad​

Answer 1

Given:

↪Two sides of the ||gm ABCD are 6cm and 4cm.

↪The height of corresponding of the base CD is 3cm.

To Find:

i) Area of ||gm

ii) Height of the corresponding to the base AD

Solution:

[Refer the attached figure for ||gm ABCD]

AB = CD = 6cm

BC = AD = 4cm

Height, AE = 3cm

i) Area of ||gm = base × Height

= 3 × 4

= 12cm²

Hence, Area of ||gm is 12m²

ii) In ∆ADF

AE = FD = 3cm

AD = 4cm

By Pythagoras Theorem

(AF)² = (AD)² - (FD)²

= (4)² - (3)²

= 16 - 9

= 7

(AF)² = 7

AF = √7cm

Hence, the height of the corresponding to the base AD is √7cm.

Answer 2

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AB = CD = 6cm

BC = AD = 4cm

Height, AE = 3cm

i) Area of ||gm = base × Height

$\implies$ 3 × 4

$\implies$ 12cm²

Hence, Area of ||gm is 12m²

ii) In ∆ADF

$\implies$AE = FD = 3cm

$\implies$AD = 4cm

By Pythagoras Theorem

(AF)² = (AD)² - (FD)²

$\implies$ (4)² - (3)²

$\implies$ 16 - 9

$\implies$ 7

$\implies$(AF)² = 7

$\implies$AF = √7cm

Hence, the height of the corresponding to the base AD is √7cm.