Question

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

Answer 1

99cm^2

Explanation:

pizza time

Answer 2

Consider parallelogram ABCD. The shorter sides are AB and CD, so
`AB=CD=√(82)` cm.

The shorter altitudes are BH=CF=9 cm.

1. Consider right triangle FCD:

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

`√(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.