Question

Find the measure of 2D, and the perimeter and area of parallelogram ABCD.

17 cm
28°
8 cm
25cm
O • • O

Answer 1

Angle D is 152 degrees. The perimeter of the parallelogram is 84 cm and the area is 200 square centimetres. So, the correct option is C.

To find the measure of angle D, we can use the fact that opposite angles of a parallelogram are equal. Since angle BAC is given as 28 degrees, So, angle BCD will also be 28 degrees. Also, angle D and angle ABC will be equal The sum of angles in a quadrilateral is 360 degrees. Substituting the given values we get:

`\angle A + \angle C + \angle D + \angle B=360`

`28+28+2(\angle D)=360`

`\angle D=(360-56)/(2)`

`\angle D= 152`

To find the perimeter of the parallelogram, we can use the formula:

P = 2(AB + BC).

Given AB = 17 cm and BC = 25 cm, the perimeter will be:

P = 2(17 + 25) = 84 cm.

To find the area of the parallelogram, we can use the formula:

Area = base x height.

Given the base AD = BC = 25 cm and the height is given as 8 cm, the area will be:

Area = 25 cm x 8 cm

= 200 square centimetres.