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nikitadnepr [17]
2 years ago
3

The Lengths of the shorter altitude and the shorter side of parallelogram are 9cm and root 82 cm, respectively. The Length of a

longer diagonal is 15 cm. What is the area of this parallelogram

Mathematics
1 answer:
levacccp [35]2 years ago
7 0

Consider parallelogram ABCD. The shorter sides are AB and CD, so AB=CD=\sqrt{82} cm.

The shorter altitudes are BH=CF=9 cm.

1. Consider right triangle FCD:

CD^2=DF^2+CF^2,

\sqrt{82}^2=9^2+FD^2,\\ \\FD^2=82-81=1,\\ \\FD=1 cm.

2. Consider right triangle FCA:

CA^2=DF^2+FA^2,

15^2=9^2+FA^2,\\ \\FA^2=225-81=144,\\ \\FA=12 cm.

3.

FA=AD+FD,\\ \\AD=12-1=11 cm.

4. Therefore, the area of parallelogram ABCD is

A_{ABCD}=AD\cdot BH=11\cdot 9=99 sq. cm.

Answer: 99 sq. cm.


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