Find the height of a trapezoid with bases 9 and 6 and an area of 120 square units
2 answers:
Answer:
Height (h) = 16 units
Step-by-step explanation:
Area of trapezium = ½ (Sum of 2 parallel lengths) * Height
Area = ½ ( a + b ) h
Given that:
a=6 units
b= 9 units
Area = 120 square units
Therefore:
120 = ½(6+9) h
120 = ½ (15) h
Multiply through by 2.
2*120 = 2*½ (15) h
240 = 15h
h = 240/15
h= 16 units
Please find the attached file for the sketch.
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<h2>Explanation:</h2>
In every rectangle, the two diagonals have the same length. If a quadrilateral's diagonals have the same length, that doesn't mean it has to be a rectangle, but if a parallelogram's diagonals have the same length, then it's definitely a rectangle.
So first of all, let's prove this is a parallelogram. The basic definition of a parallelogram is that it is a quadrilateral where both pairs of opposite sides are parallel.
So let's name the vertices as:
First pair of opposite sides:
<u>Slope:</u>
Second pair of opposite sides:
<u>Slope:</u>
So in fact this is a parallelogram. The other thing we need to prove is that the diagonals measure the same. Using distance formula:
So the diagonals measure the same, therefore this is a rectangle.