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33 votes
33 votes
11.) In the given figure, IJKL is an isosceles trapezoid with base LK = 16 and 1) = 8.If I = R = 5, then what is the area of the trapezoid?A 24 cmB 36 cm1C 45 cmKD 89 cm?GO ON12.) What is the value of x?

11.) In the given figure, IJKL is an isosceles trapezoid with base LK = 16 and 1) = 8.If-example-1
User Raychi
by
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1 Answer

20 votes
20 votes

Area of an trapezoidal is express as :


Area\text{ = }\frac{Sum\text{ of Parallel sides}}{2}* Height\text{ of trapezoid}

So, to find the height of trapezium we draw a perpendicular from J to the base line LK and a perpendicular from I to the base line LK such that the MN= IJ

So, We have two right triangle JNK and IML

Apply Pythogaras in any one of the right triangle and find the length of perpendicular

In triangle JNK


\begin{gathered} \text{From Pythagoras ,} \\ \text{Hypotenuse }^2+Perpendicular^2_{}+Base^2 \\ JK^2=JN^2+NK^2 \\ \text{Substitute the valus and solve for JN,} \\ 5^2=JN^2+4^2 \\ JN^2=25-16 \\ JN^2=9 \\ JN=3 \\ \text{ So, The perpendicular of triangle JN is 3} \end{gathered}

Since, the perpendicular JN is also the height of trapezium,

Substitute the values

Height JN =3

Parallel Sides IJ = 8 and LK = 16

So, the Area of Trapezium will be


\begin{gathered} \text{Area of trapezium IJKL =}\frac{Sum\text{ of parallel Sides}}{2}* Height \\ \text{Area of trapezium IJKL =}\frac{IJ\text{ +LK}}{2}* JN \\ \text{Area of trapezium IJKL =}(8+16)/(2)*3 \\ \text{Area of trapezium IJKL =}(24)/(2)*3 \\ \text{Area of trapezium IJKL =12}*3 \\ \text{Area of trapezium IJKL =}36cm^2 \end{gathered}

Answer : B) 36 cm²

11.) In the given figure, IJKL is an isosceles trapezoid with base LK = 16 and 1) = 8.If-example-1
User Denizeren
by
3.2k points
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