Question

Area of a trapezium is 16 sqcm.Length of one parallel side is 5 cm and distance between two parallel sides is 4 cm.Find the length of the other parallel side.Try to draw this trapezium on agraph paper and check the area.

Answer 1

Answer on Question #49550 – Math – Geometry

Area of a trapezium is 16 sq cm. Length of one parallel side is 5 cm and distance between two parallel sides is 4 cm. Find the length of the other parallel side. Try to draw this trapezium on a graph paper and check the area.

Solution:

$A = 16\, \text{cm}^2$ – area of a trapezium;

$a = 5\, \text{cm}$ – length of one parallel side;

$b$ – length of the other parallel side;

$h = 4\, \text{cm}$ – distance between two parallel sides;

The area of a trapezium is given by the formula:

$$A = \frac{(a + b)}{2} h,$$

hence

$$2A = a h + b h$$ $$b = \frac{2A - a h}{h} = \frac{2A}{h} - a = \frac{2 \cdot 16\, \text{cm}^2}{4\, \text{cm}} - 5\, \text{cm} = 3\, \text{cm}$$

Answer: length of the other parallel side is equal to $3\, \text{cm}$.

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