Question

Work out the area of the trapezium ABDE

Answer 1

the two triangles seen in the picture are simular (congruent) and one is enlarged.

scale factor= 9÷6 = 1.5

8×1.5 =12 (the side length of the triangle)

12-8=4 (bottom side length of trapezium)

area of trapezium= 1/2× ((a+b)×h)

1/2×((6+9)×4)=24cm^2

Answer 2

The trapezium is a part of a right angled triangle. The area of the trapezium ABDE is 30 square centimeter.

Given information:

ACE is a right angled triangle and ABDE is a trapezium with angle E equal to $90^{\circ}$.

The length of side BD is 6 cm, the length of side CD is 8 cm, and length of side AE is 9 cm.

BD is perpendicular to CE. So, BD will be parallel to the side AE as they both are perpendicular on the same side CE.

Now, according to Thales theorem, the sides of triangle ACE and BCD will be in same ratio because BD is parallel to AE.

So, the length of CE will be calculated as,

$\dfrac{BD}{AE}=\dfrac{CD}{CE}\\\dfrac{6}{9}=\dfrac{8}{CE}\\CE=12$

So, the length of side DE will be,

$DE=CE-CD\\DE=12-8=4$

Now, in the trapezium ABDE, the length of parallel sides is $BD=6, \; AE=9$ and the height DE of the trapezium is 4 cm.

Thus, the area of the trapezium will be,

$A=\dfrac{1}{2}(BD+AE)\times DE\\A=\dfrac{1}{2}(6+9)\times 4\\A=30$

Therefore, the area of the trapezium ABDE is 30 square centimeter.

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https://brainly.com/question/23141826