Question

The parallel sides of a Trapezium are 20 cm and 13 cm .its non parallel sides are 10 cm each. find the area of trapezium

Answer 1

Hello......... ^_^

Here is your answer...

Given :-
parallel sides of a trapezium are 20cm and 13cm
non-parallel side are 10cm


I named the trapezium ABCD ( in the attached image)
two parallel sides = AB = 13cm and DC =20cm
non-parallel side = AD = BC = 10cm each

( draw a line parallel to BC ) ,BC = AE = 10cm

draw another line which is perpendicular to DC

now,
AB = EC = 13cm
DE = 20 - 13 = 7cm
(as AF is perpendicular to DC it divides DF, and FE equally )
so,
DF = FE = 7/2
DF = 3.5cm and FE = 3.5cm

AFE triangle and AFD triangle are right angled triangle.

triangle AFE
$= {(AF )}^{2} + {(FE )}^{2} = {( AE)}^{2} \\ \\ = {(AF )}^{2} + {(3.5)}^{2} = {(10)}^{2} \\ \\ = {(AF )}^{2} + 12.25 = 100 \\ \\ = {(AF )}^{2} = 100 - 12.25 \\ \\ = {(AF )}^{2} = 87.75 \\ \\ = AF = \sqrt{87.75 } \\ \\ = AF = 9.36$

the height (AF) = 9.3cm

area of trapezium
$= \frac{1}{2} \times (sum \: \: of \: \: two \: \: parallel \: \: sides) \times distance \: \: between \: them \\ \\ = \frac{1}{2} \times (13 + 20) \times 9.3 \\ \\ = \frac{1}{2} \times 33 \times 9.3 \\ \\ = \frac{33 \times 9.3}{2} \\ \\ = \frac{306.9}{2} \\ \\ = 153.45$
$Area \: \: of \: \: trapezium = 153.45 {cm}^{2}$




hope it helps............... ^_^

Answer 2

ABCD be the given trapezium in which AB = 20 cm, DC = AE= 13 cm, BC = 10 cm and AD = 10 cm. 


Through C, draw CE || AD, meeting AB at E. 

Draw CF ⊥ AB. 

Now, EB = (AB - AE) = (AB - DC) 

EB = (20- 13) cm = 7 cm; 

CE = AD = 10 cm; AE = DC = 10 cm. 

Now, in ∆EBC, we have CE = BC = 10 cm. 

It is an isosceles triangle. 

Also, CF ⊥ AB

So, F is the midpoint of EB. 

Therefore, EF = ¹/₂ × EB = 1/2× 7 = 3.5 cm. 

Thus, in right-angled ∆CFE, we have CE = 10 cm, EF = 3.5 cm. 

By Pythagoras’ theorem, we have 

CF = [√CE² - EF²] 

CF = √(10² - (3.5)²) 

CF= √100-12.25= √87.75 = 9.36 cm

CF= 9.36 cm

Thus, the distance between the parallel sides is 9.36 cm. 

Area of trapezium ABCD = ¹/₂ × (sum of parallel sides) × (distance between them) 

Area of trapezium ABCD = ¹/₂ × (20 + 13) × 9.36 cm² 

Area of trapezium ABCD = 1/2×(33)× 9.36

Area of trapezium ABCD=  154056 cm² 

Hence, Area of trapezium ABCD= 154.56 cm²