Question

if the base of this parallelogram is the side that is 6 units long, what is the length of the matching height? 6 units 4.8 units 4 units 5 units

Explanation:

Step1: Recall parallelogram height definition

Height is perpendicular to the base. The base here is 6 units (the horizontal side). The dashed line (height) perpendicular to the 6 - unit base? Wait, no, the vertical dashed line is perpendicular to the 6 - unit base (since the base is horizontal, the vertical dashed line is height). Wait, looking at the diagram, the height corresponding to base 6 is the vertical dashed line with length 4? Wait, no, wait. Wait, the parallelogram has base 6 (horizontal) and the height perpendicular to it is the vertical segment of length 4? Wait, but let's check the area. Alternatively, the height must be perpendicular to the base. The base is 6 units (the side of length 6), so the height is the segment perpendicular to this base. From the diagram, the vertical dashed line (with right angle) is perpendicular to the 6 - unit base, so its length is 4 units? Wait, no, wait the options: 6, 4.8, 4, 5. Wait, maybe I misread. Wait, the other side is 5. Wait, maybe the height corresponding to base 6 is 4? Wait, let's think again. The height is a perpendicular segment from a vertex to the base (or its extension). In the diagram, the base is 6 (the two horizontal sides), and the height perpendicular to it is the vertical dashed line with length 4 (since there's a right angle there). So the matching height for base 6 is 4 units? Wait, but there's a dashed line of 4.8 with a right angle on the slant side. Wait, no: the base is 6 (the horizontal side), so the height must be perpendicular to the horizontal side (base 6). So the vertical dashed line (length 4) is perpendicular to the horizontal base (length 6). So the height is 4 units? Wait, but let's confirm. The area of a parallelogram is base × height. If we take base 5, the height would be 4.8 (since 5×4.8 = 24). Then if base is 6, height would be 24÷6 = 4. Ah, that makes sense. So area is 5×4.8 = 24. Then for base 6, height = 24÷6 = 4. So the height is 4 units.

Step2: Calculate height using area

First, find the area using the other base and height. Base = 5, height = 4.8. Area \( A = 5\times4.8 = 24 \). Then, for base = 6, height \( h=\frac{A}{6}=\frac{24}{6}=4 \).

Answer:

4 units