(60 POINTS) Given parallelogram
2 answers:
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Answer:
The area of the parallelogram is 108 inches² <em>OR</em> 0.75 foot²
Step-by-step explanation:
* Lets revise the properties of the parallelogram
- Each two opposite bases are are parallel
- Each two opposite bases are equal in length
- Each two opposite angles are equal in measure
- Each two adjacent angles are supplementary (their sum = 180°)
- Its two diagonals bisect each other
- Each base has an altitude (height) drawn from the opposite
base to it
* Look to the attached figure to more understand
- The area of the parallelogram is the product of the length of one
of its base and the corresponding altitude (height)
∵ Area = B1 × H1 ⇒ OR ⇒ Area = B2 × H2
∵ B1 = 1 1/2 feet
∵ H1 = 6 inches
- The base and the height have different units, so we must
change the unit of one of them to the other
∵ 1 foot = 12 inches
∵ B1 = 1 1/2 = 1.5 feet
∴ B1 = 1.5 × 12 = 18 inches
∴ A = 18 × 6 = 108 inches²
* The area of the parallelogram is 108 inches²
OR
∵ B1 = 1 1/2 = 1.5 feet
∵ H1 = 6 inches
∴ H1 = 6 ÷ 12 = 1/2 = 0.5 foot
∴ A = 1.5 × 0.5 = 0.75 foot²
* The area of the parallelogram is 0.75 foot²
Answer:
ΔFHK and ΔGHJ are the similar triangles by SAS similarity theorem.
Step-by-step explanation:
Picture for the given question is missing; find the picture attached.
If and ∠H ≅ ∠H
Then ΔFHK ~ ΔGHJ
Since, and ∠H ≅ ∠H [By reflexive property]
Therefore, ΔFHK and ΔGHJ are the similar triangles by SAS similarity theorem.
Option (3) will be the answer.
