Question

ABCD is a parallelogram whose adjacent sides AB = 48 cm and BC = 14 cm. One of its diagonals AC = 50 cm. Then Find :

(1) the area of the parallelogram ABCD.

(2) the distance between the longer sides.

(3) the distance between the shorter sides.

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Answer 1

✠ Gɪᴠᴇɴ :: –

• ABCD ɪs ᴀ ᴘᴀʀᴀʟʟᴇʟᴏɢʀᴀᴍ .
• Iᴛs ᴀᴅᴊᴀᴄᴇɴᴛ sɪᴅᴇs :: – AB ➪ 48ᴄᴍ ᴀɴᴅ BC ➪ 14ᴄᴍ.
• Oɴᴇ ᴏғ ɪᴛs ᴅɪᴀɢᴏɴᴀʟs ɪs AC ➪ 50ᴄᴍ.

✠ Exɪɢᴇɴᴄʏ ᴛᴏ ғɪɴᴅ :: –

• (1) Tʜᴇ ᴀʀᴇᴀ ᴏғ ᴘᴀʀᴀʟʟᴇʟᴏɢʀᴀᴍ ABCD.
• (2) Tʜᴇ ᴅɪsᴛᴀɴᴄᴇ ʙᴇᴛᴡᴇᴇɴ ᴛʜᴇ Lᴏɴɢᴇʀ Sɪᴅᴇs.
• (2) Tʜᴇ ᴅɪsᴛᴀɴᴄᴇ ʙᴇᴛᴡᴇᴇɴ ᴛʜᴇ Sʜᴏʀᴛᴇʀ Sɪᴅᴇs.

✠ Fᴏʀᴍᴜʟᴀᴇ ᴜsᴇᴅ :: –

• s ➠ ½ (AB + BC + AC)
• Area of ΔABC ➠ √(s (s - a) (s - b) (s - c))
• Area of parallelogram ABCD ➠ 2 × (Area of ΔABC)
• Distance between the longer sides ➠ Area of parallelogram ABCD = AB × h₁
• Distance between the shorter sides ➠ Area of parallelogram ABCD = BC × h₂

✠ Exᴘʟᴀɴᴀᴛɪᴏɴ :: –

(i) Tʜᴇ ᴀʀᴇᴀ ᴏғ ᴘᴀʀᴀʟʟᴇʟᴏɢʀᴀᴍ ABCD :: –

❍ Finding, the value of s.

✠ Substitute the values :: –

➠ s ➠ ½ (AB + BC + AC) cm

➠ s ➠ ½ (48 + 14 + 50) cm

➠ s ➠ ½ (112) cm

➠ s ➠ ¹¹²⁄₂ cm

➠ s ➠ 56 cm. [ .°. Value of s is 56 cm.]

❍ Finding, Area of ΔABC ::–

✠ Substitute the values :: –

➠ ΔABC ➠ √(s (s - a) (s - b) (s - c))

➠ ΔABC ➠ √(56 × 8 × 42 × 6)cm²

➠ ΔABC ➠ √((8 × 7) × 8 × (6 × 7) × 6)cm²

➠ ΔABC ➠ 8 × 7 × 6 cm²

➠ ΔABC ➠ 336 cm². [ .°. Area of ΔABC is 336 cm².]

✰ Finding, Area of parallelogram ABCD ::–

✠ Substitute the values :: –

➠ Area of parallelogram ABCD ➠ 2 × (Area of ΔABC)

➠ Area of parallelogram ABCD ➠ 2 × (336)cm²

➠ Area of parallelogram ABCD ➠ 672 cm².

[ .°. Hence, Area of parallelogram ABCD is 672 cm².]

(ii) Tʜᴇ ᴅɪsᴛᴀɴᴄᴇ ʙᴇᴛᴡᴇᴇɴ ᴛʜᴇ Lᴏɴɢᴇʀ Sɪᴅᴇs :: –

✠ Substitute the values :: –

➠ Distance between the longer sides ➠ Area of parallelogram ABCD = AB × h₁

➠ Distance between the longer sides ➠ 672 = 48 × h₁

➠ Distance between the longer sides ➠ h₁ = ⁶⁷²⁄₄₈ cm

➠ Distance between the longer sides ➠ h₁ = 14 cm.

[ .°. Hence, Distance between the longer sides is 14 cm.]

(iii) Tʜᴇ ᴅɪsᴛᴀɴᴄᴇ ʙᴇᴛᴡᴇᴇɴ ᴛʜᴇ Sʜᴏʀᴛᴇʀ Sɪᴅᴇs :: –

✠ Substitute the values :: –

➠ Distance between the longer sides ➠ Area of parallelogram ABCD = BC × h₂

➠ Distance between the longer sides ➠ 672 = 14 × h₂

➠ Distance between the longer sides ➠ h₁ = ⁶⁷²⁄14 cm

➠ Distance between the longer sides ➠ h₁ = 48 cm.

[ .°. Hence, Distance between the shorter sides is 48 cm.]

I hope that it helps you ♡♡

Answer 2

Answer:

Area of parallelogram

= base × height

=27×12cm

= 324cm

2

Area = b×h

324=36×h

36

324

h= 9 cm

Step-by-step explanation:

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