Name: Area of Polygon by Triangulation
Uploaded: 2019-07-19
Duration: 11 min 5 s
Description: How can you calculate the area of polygons when you forget its formula? Simple! Break it down into shapes that you know the formula for. Watch to learn how!

Question

The parallel sides of a trapezium are 25 cm and 13 cm. Its non-parallel sides equal 10 cm. What is the area of the trapezium?

Accepted Answer

ABCD is a trapezium in which $A B = 25 c m, C D = 13 c m (A B | | C D)$ , and

BC=AD = 10 cm ,
draw perpendiculars CP and DQ from C and D on AB.

PB = QA as BC = AD =10 cm.
Let $P B = Q A = x c m . A B = Q A + Q P + P B$ ,
putting
$A B = 25 c m, P B = Q A = x c m, a n d Q P = C D = 13 c m, 25 = x + 13 + x . = > 2 x = 25 - 13 = > x = 12 / 2 = 6 c m .$

In right angled triangle CPB ,
$C P^{2} + P B^{2} = B C^{2} o r, C P^{2} + 6^{2} = 10^{2} o r, C P^{2} = 100 - 36 = 64 o r, C P = 8 c m .$
Area of trapezium ABCD = $1 / 2 (A B + C D) \times C P = 1 / 2 (25 + 13) \times 8 c m^{2} .$
$= 1 / 2 (38 \times 8) = 152 c m^{2} .$

The parallel sides of a trapezium are 25 cm and 13 cm. Its non-parallel sides equal 10 cm. What is the area of the trapezium?

Important Questions on Perimeter and Area of Triangles and Quadrilaterals

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