Question

find the area of the trapezium E F G H having measurement as shown in the figure​

Answer 1

Area of trapezium EFGH = $\bold{348\ cm^2}$

Step-by-step explanation:

Given,

EFGH is a trapezium.

In triangle EFG,

∠EFG = 90°

By Applying Pythagoras Theorem

$(EF)^2+ (GF)^2 = (EG)^2$

$(EF)^2 + (35)^2 = (37)^2$

$(EF)^2 + 1225=1369$

$(EF)^2 = 1369-1225$

$(EF)^2 = 144$

Taking square root on both sides,

EF = 12 cm

⇒Height of trapezium EFGH = 12 cm

$Area\ of\ trapezium\ EFGH = \frac{1}{2}\times (Sum\ of\ opposite\ parallel\ sides)\times Height$

Area of trapezium EFGH = $\frac{1}{2}\times (23+35)\times 12$

                                         =$\frac{1}{2}\times 58 \times 12$

                                         = $\bold{348\ cm^2}$

Answer 2

Step-by-step explanation:

Using pythagoras Theoram

H² = P² + B²

37² = P² + 35²

1369 = P² + 1225

P² = 1369 – 1225

P² = 144

P = square root of 144

P = 12

Area = 1/2 × h × ( a + b )

area = 1/ 2 × 12 × ( 23 + 35 )

Area = 1/ 2 × 12 × 58

Area = 6 × 58

Area = 348 cm².

hope it's help you