Question
Trapezium given below; find its area.
✓
Answer
For the $\triangle EBC,$
$S = 19\ cm$
Area of $\triangle EBC = \sqrt{19 \times(19-16) \times(19-12) \times(19-10)}$
$=\sqrt{19 \times 3 \times 7 \times 9}$
$=59.9 \text { sq. } \ cm $
Let $h$ be the height.
Area of $\triangle EBC=\frac{1}{2} \times 12 \times h$
$\Rightarrow 59.9 = 6\ h$
$\Rightarrow h =\frac{59.9}{6}=9.98 \ cm$
Area of $\text{ABCD} =\frac{1}{2} \times(20+32) \times 9.98$
$=\frac{1}{2} \times 52 \times 9.98$
$=259.48 \ cm ^2$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Find the amount and the compound interest on the following :$Rs.15000$ for $2$ years at $8\%$ per annum compounded semi$-$annually.
→In $\triangle ABC, D$ and $E$ are two points on the side $AB$ such that $AD = DE = EB$. Through $D$ and $E,$ lines are drawn parallel to $BC$ which meet the side $AC$ at points $F$ and $G$ respectively. Through $F$ and $G$, lines are drawn parallel to $AB$ which meet the side $BC$ at points $M$ and $N$ respectively.Prove that $BM = MN = NC.$
→Draw the graph for the equation, given below : $3x + 2y = 6$
→Solve the following systems of equation by using the method of cross multiplication:
$2 x+3 y=17,3 x-2 y=6$
→$2 x+3 y=17,3 x-2 y=6$
Evaluate the following: $\frac{5 \sec 68^{\circ}}{\operatorname{cosec} 22^{\circ}}+\frac{3 \sin 52^{\circ} \sec 38^{\circ}}{\cot 51^{\circ} \cot 39^{\circ}}$
→Find the mean and median of all the positive factors of $72.$
→6 men and 8 boys can finish a piece of work in 14 days while 8 men and 12 boys can do it in 10 days. Find the time taken by one man alone and that by one boy alone to finish the work.
If $A = 30^\circ$show that: $ \frac{\cos ^3 A-\cos 3 A}{\cos A}+\frac{\sin ^3 A+\sin 3 A}{\sin A}=3 $
→In the following figure$, \angle B A C=60^{\circ}$ and $\angle A B C=65^{\circ}$.
Prove that:$(i) \ CF > AF(ii) \ DC > DF$
→Prove that:$(i) \ CF > AF(ii) \ DC > DF$
Factorise the following:$(a^2 - b^2)(c^2 - d^2) - 4abcd$
→