Altitude ED and FB are both a cm long. The distance between their feet is b cm. Find the area of the parallelogram ABCD.
Share
Altitude ED and FB are both a cm long. The distance between their feet is b cm. Find the area of the parallelogram ABCD.
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Step-by-step explanation:
Area of a parallelogram = Base × Height
⇒ 30 cm2 = 6 cm × AE
⇒ AE =
Using angle sum property in ΔAED:
∠ADE + ∠DEA + ∠EAD = 180°
⇒ 60° + 90° + ∠EAD = 180°
⇒ 150° + ∠EAD = 180°
⇒ ∠EAD = 180° − 150° = 30°
Thus, the angles of ΔAED are 30°, 60° and 90°.
Therefore, the ratio of the lengths of the sides of ΔAED is 1::2.
Thus, the length of other side of the parallelogram is cm.
Note: We can also draw the figure by taking ∠ADE = 60° and AD = 6 cm.