The length of the median of the trapezoid is [tex]\boxed{12.80}.[/tex]
Further explanation:
The median is a line that divides the trapezoid into two equal halves that has same area.
The formula to calculate the median of the trapezoid can be expressed as follows,
[tex]\boxed{{\text{Median}}=\sqrt {A{C^2} + B{D^2}}}[/tex]
Here, AC and BD are the diagonals of the trapezoid.
Given:
The diagonals of a trapezoid are perpendicular to each other and have lengths 8 and 10.
Explanation:
The lengths of the diagonals are 8 and 10.
The length of the median of the trapezoid can be calculated as follows,
[tex]\begin{aligned}{\text{Median}}&= \sqrt {A{C^2} + B{D^2}}\\&=\sqrt {{8^2} + {{10}^2}}\\ &= \sqrt {64 + 100}\\&= \sqrt {164}\\&= 12.80\\\end{aligned}[/tex]
The length of the median of the trapezoid is [tex]\boxed{12.80}.[/tex]
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Answer details:
Grade: Middle School
Subject: Mathematics
Chapter: Trapezoid
Keywords: triangle, triangle pair, equal angles, sides, area, trapezoid, two triangles, bases, intersecting, diagonal, segment, sector, minor segment, median, perpendicular, lengths, 8, 10, length of the median.
