Question

PQRS is a trapezium in which PS∥QR and QP⊥PS. If PS=25 cm, QR=35 cm and PQ=24 cm, find the area of the trapezium.

Answer 1

Answer:

ar of trapezium= 1/2(sum of parallel sides )× height

=1/2(12×35×60)×29

=1(12×35×30)×29

=(12,600)×29

=365,400cm

Step-by-step explanation:

Answer 2

 

• PQRS is a trapezium

• PS ∥ QR

• QP⊥PS

• PS = 25 cm

• QR = 35 cm

• PQ = 24 cm

 

• Area of the trapezium PQRS

 

• Area of Trapezium PQRS = 720 cm²

 

Well, There are two ways to solve this question using :

• Area of the trapezium formula

• Area of Rectangle + Area of Right angled Triangle

Using Area of the trapezium formula :

Area of Trapezium =  1/2 × Sum of Parallel Sides × Distance Between Them

⇒ Area of Trapezium = 1/2 × Sum of Parallel Sides × Height

⇒ Area of Trapezium = 1/2 × (PS + QR) × Heigh

⇒ Area of Trapezium = 1/2 × (25 cm + 35 cm) × Height

⇒ Area of Trapezium = 1/2 × (60 cm) × Height

⇒ Area of Trapezium = 1/2 × 60 cm × Height

⇒ Area of Trapezium = 1/2 × 60 cm × PQ

⇒ Area of Trapezium = 1/2 × 60 cm × 24 cm

⇒ Area of Trapezium = 1/2 × 60 cm × 24 cm

⇒ Area of Trapezium = 1/2 × 1440 cm²

⇒ Area of Trapezium = 1440/2  cm²

⇒ Area of Trapezium = 720  cm²

Using Area of Rectangle + Area of Right angled Triangle :

• First We need to make use of one more Alphabet or Variable as a point to use this method

Assign variable "T" straightly opposite to point S

Then the Trapezium PQRS is divided into :

• Rectangle PQTS

• Right Angled Triangle STR

Then, This formula becomes True :

• Area of Trapezium PQRS = Area of Rectangle PQTS + Area of Right angled Triangle STR

✭ First Let's solve for Area of Rectangle PQTS

Area of Rectangle PQTS = Length × Breadth

⇒ Area of Rectangle PQTS = 25 cm × 24 cm

⇒ Area of Rectangle PQTS = 600 cm²

✭ Now solve for Area of Right angled Triangle STR

Area of Right angled Triangle STR = 1/2 × Base × Height

⇒ Area of Right angled Triangle STR = 1/2 × 24 cm × (35 cm - 25 cm)

⇒ Area of Right angled Triangle STR = 1/2 × 24 cm × 10 cm

⇒ Area of Right angled Triangle STR = 1/2 × 240 cm²

⇒ Area of Right angled Triangle STR = 240/2 cm²

⇒ Area of Right angled Triangle STR = 120 cm²

✭ Finally Solve For Area of Trapezium PQRS

Area of Trapezium PQRS

= Area of Rectangle PQTS + Area of Right angled Triangle STR

⇒ Area of Trapezium PQRS = 600 cm² + 120 cm²

⇒ Area of Trapezium PQRS = 720 cm²

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