Question

the parallel sides of a trapeziym are 20 cm and 10 cm. its nonparallel sides are both equal. each being 13 cm . find the area of the rrapezium. plzzzzz​

Answer 1

Answer:

area = 1/2 * sum of parallel sides * height

Step-by-step explanation:

Given :

ABCD is the given trapezium.

AB = 20 cm

DC = AE = 10 cm

BC = 13 cm

AD = 13 cm

Draw CF ⊥ AB.

Now,

EB = (AB - AE) = (AB - DC)

= (20- 10) cm = 10 cm

In ∆EBC, we have

CE = BC = 13 cm

EF = ½ × EB

= ½ × 10 = 5 cm

In right-angled ∆CFE, we have

CE = 13 cm, EF = 5 cm

By Pythagoras theorem, we have

CF = √(CE² - EF²)

= √(13² - 5²)

= √(169 - 25)

= √144 = 12 cm

Find the area of trapezium ABCD :-

Area of trapezium = ½ × (sum of parallel sides) × height square unit

= ½ × (20 + 10) × 12 cm²

= ½ × 30 × 12 cm²

= 15 × 12 cm²

= 180 cm²

Hence,

Area of trapezium = 180 cm²