Question

The parallel sides of a trapezium are 15m and 10m long and its non-parallel sides are 8m and 7m long find the area of trapezium

Answer 1

Answer:

Area of trapezium is $50\sqrt{3}\text{ cm}^2$

Step-by-step explanation:

The parallel sides of a trapezium are 15 m and 10 m long and its non-parallel sides are 8 m and 7 m long.

Please see the attachment for figure.

Draw two altitute on side AB from point D and C at point E and F respectively.

Let height of trapezium be h cm

Therefore, DE=CF=h

DE and CF are parallel and perpendicular lines.

Therefore, DEFC is a rectangle.

Hence, DC=EF = 10 cm

Let FB be x cm

AE=5-x

In ΔAED, ∠AED=90°

AD=8 cm, DE=h cm and AE= (5-x) cm

Using pythagoreous theorem

$AD^2=DE^2+AE^2$

$8^2=h^2+(5-x)^2$---------------------(1)

In ΔCFB, ∠CFB=90°

BC=7 cm, CF=h cm and FB= x cm

Using pythagoreous theorem

$BC^2=CF^2+FB^2$

$7^2=h^2+x^2$--------------------------(2)

Subtract (1) - (2)

$64-49 = (5-x)^2 - x^2$

$15=5(5-2x)$

$x=1$

Put x=1 into equation 1 and solve for h

[tex[8^2=h^2+4^2[/tex]

$h=4\sqrt{3}$

Area of trapezium = $\frac{1}{2}\times h\times (AB+CD)$

Area of trapezium = $\frac{1}{2}\times 4\sqrt{3}\times (10+15)$

Area of trapezium = $50\sqrt{3}\text{ cm}^2$