Question

in adjoining figure, AP perpendicular BC, AD|| BC, Then Find A( Triangle ABC): A( Triangle BCD).

Answer 1

Concept:

Area of triangle = 1/2 × b × h

ABC and BCD are triangle lying between same parallels and having the same base BC.

A1 :
Area of triangle ABC = 1/2 × BC × AP

A2:
Area of triangle BCD = 1/2 × BC × AP

Now

A1 : A2 = 1 : 1

Answer 2

ᴀʀᴇᴀ ᴏғ ᴛʀɪᴀɴɢʟᴇ = 1/2 × ʙ × ʜ

ᴀʙᴄ ᴀɴᴅ ʙᴄᴅ ᴀʀᴇ ᴛʀɪᴀɴɢʟᴇ ʟʏɪɴɢ ʙᴇᴛᴡᴇᴇɴ sᴀᴍᴇ ᴘᴀʀᴀʟʟᴇʟs ᴀɴᴅ ʜᴀᴠɪɴɢ ᴛʜᴇ sᴀᴍᴇ ʙᴀsᴇ ʙᴄ. 

ᴀ1 :
ᴀʀᴇᴀ ᴏғ ᴛʀɪᴀɴɢʟᴇ ᴀʙᴄ = 1/2 × ʙᴄ × ᴀᴘ

ᴀ2:
ᴀʀᴇᴀ ᴏғ ᴛʀɪᴀɴɢʟᴇ ʙᴄᴅ = 1/2 × ʙᴄ × ᴀᴘ

ɴᴏᴡ 

ᴀ1 : ᴀ2 = 1 : 1