Question

Area of ABCD is ______.

Options

• 244 cm²

• 122 cm²

• 114 cm²

• 142 cm²

Answer 1

Area of ABCD is 114 cm².

Explanation:

Given:

• BC = 12 cm   ...(One side of triangle ABC)
• AB = 9 cm   ...(Height of triangle ABC, since angle B is 90°)
• CD = 8 cm   ...(One side of triangle ADC)
• AD = 17 cm   ...(Hypotenuse of triangle ADC, with right angle at C)

First, find the height of triangle ADC which is perpendicular from C to AD.

Using the Pythagorean theorem to find AC:

In triangle ADC:

`AC = sqrt(AD^2 - CD^2)` 

= `sqrt(17^2 - 8^2)` 

= `sqrt(289 - 64)`

= `sqrt(225)`

= 15 cm

Now, Area of triangle ABC

= `1/2 xx AB xx BC` 

= `1/2 xx 9 xx 12`

= 54 cm²

Area of triangle ADC

= `1/2 xx CD xx AC` 

= `1/2 xx 8 xx 15`

= 60 cm²

So, Area of ABCD

= Area(ABC) + Area(ADC) 

= 54 + 60

= 114 cm²