Find the area of a parallelogram if its heights are 6 cm and 8 cm, and the perimeter is 42 cm

1. The tops of the parallelogram A, B, C, D. Height BK = 6 cm – drawn to the side AD.

Height BE = 8 cm – drawn to the side of the CD.

2. Let’s designate the AD side by the “a” index, the CD side by the “b” index.

3. Let’s compose two equations:

(1) 2a + 2b = 42; a + b = 21;

(2) 6a = 8b; 6a – 8b = 0; 3a – 4b = 0;

4. Multiply the first equation by 3:

3a + 3b = 63;

5. Subtract the second equation from the resulting equation:

3a + 3b – 3a + 4b = 63;

7c = 63;

h = 9 cm.

6. Substitute in = 9 in the first equation:

a + 9 = 21;

a = 12 cm.

7. Calculate the area (S) of a given parallelogram:

S = 12 x 6 = 72 cm or 9 x 8 = 72 cm².

Answer: the area of ​​a given parallelogram is 72 cm².