Question

*The length of the shorter altitude and the shorter side of a parallelogram are 9cm and 82 cm. The length of a longer diagonal is 15 cm. What is the area of this parallelogram?

Answer 1

The area of the parallelogram is 738 cm^2.

Step-by-step explanation:

To find the area of a parallelogram, we need to multiply the length of the base (one of the sides) by the length of the corresponding altitude (the perpendicular distance between the base and the opposite side). In this case, the shorter side of the parallelogram is given as 82 cm, and the length of the shorter altitude is given as 9 cm. Therefore, the area of the parallelogram can be calculated as follows:

Area = Base × Altitude = 82 cm × 9 cm = 738 cm2

Answer 2

Refer to the image attached.

Given: Altitude AC = 9 cm, Diagonal AD = 15 cm, side AB = 82 cm.

To find: Area of parallelogram

Solution:

Since, area of parallelogram = base
`*` height

=
`BD * AC`

We have to determine the base BD.

Consider the triangle ABC,

by Pythagoras theorem,

`(AB)^2 = (BC)^2 + (AC)^2`

`(82)^2 = (BC)^2 + (9)^2`

`6724-81= (BC)^2`

BC = 81.5 cm

Now, Consider the triangle ACD,

by Pythagoras theorem,

`(AD)^2 = (AC)^2 + (CD)^2`

`(15)^2 = (9)^2 + (CD)^2`

`225-81= (CD)^2`

CD = 12 cm

Now, base BD = BC + CD

= 81.5+12

= 93.5 cm

Area of parallelogram = BD
`* AC`

= 93.5 x 9

= 841.5 square centimeters.

Therefore, the area of parallelogram is 841.5 square centimeters.