Question

The parallel lines of a trapezium are 25 cm and 11cm ,while its non-parallel sides are 15 cm and 13 cm .Find the area of trapezium.

Answer 1

Question 21766

The parallel lines of a trapezium are 25 cm and 11cm ,while its non-parallel sides are 15 cm and 13 cm .Find the area of trapezium.

Solution.

Let $ABCD$ be a trapezium and let $BH$ and $CK$ be the heights. We lose no generality assuming that $AB=15cm,CD=13cm$. It is clear that

$AH+KD=AD-BC=25-11=14$cm and $BH=CK$.

Since the triangles $ABH$ and $CKD$ are right triangles, it follows from the Pythagorean Theorem that

$AB^{2}-AH^{2}=CD^{2}-KD^{2}$.

Taking into account that $AH=14-KD$, we get $225-(14-KD)^{2}=169-KD^{2}$

Thus

$225-196+28KD-KD^{2}=169-KD^{2}$

and so $KD=5$. Hence $BH=\sqrt{CD^{2}-KD^{2}}=\sqrt{169-25}=12$.

Then the area of the trapezium

$S=\frac{AD+BC}{2}BH=\frac{25+11}{2}12=216cm^{2}.$

Answer. the area of the trapezium $216cm^{2}$.

##