Find the area of the parallelogram 𝐴𝐵𝐶𝐷 where 𝐴𝐵 equals 8.3 centimeters.
We’re looking for the area of a parallelogram. And the area of a parallelogram is found by multiplying the base times the height. The base and the height of a parallelogram must be perpendicular to each other. This is the space. This is the parallelogram we’re trying to find the area of, 𝐴𝐵𝐶𝐷.
Our problem also told us that the lateral sides measure 8.3 centimeters. However, we cannot use these lateral sides to find the area of our parallelogram. The lateral sides of this parallelogram are not perpendicular to the bases. The height of this parallelogram is 7.7 centimeters. It is the distance between side 𝐴𝐷 and side 𝐵𝐶. Since the height 7.7 centimeters is the perpendicular distance between line 𝐴𝐷 and line 𝐵𝐶, we know that 8.8 is the base. We plug those two values into our formula. We multiply 8.8 times 8.7 and we find that the area of this parallelogram is 67.76 centimeters squared.