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

✯ ᴀɴsᴡᴇʀ ✯

★ given →

• PQRS is a trapezium,
• PS || QR
• PS = 25cm
• QR = 35cm
• PQ = 24cm

★ to find →

• area of the trapezium?

★ solution →

➪ we know that,

$\boxed{ \tt{area \: of \: trapezium = \frac{1}{2} (sum \: of \: parallel \: sides) \times height}} \\ \\ \tt{ : \implies \: \: area \: = \frac{1}{2} (a + b) \times h} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

here,

a = PS = 25cm

b = RQ = 35cm

h = PQ = 24cm

➪ now substitute all these values in formula;

$: \implies area = \frac{1}{2} \times (25 + 35) \times 24 \\ \\ : \implies \: area = \frac{1}{ \cancel{2}} \times 60 \times \cancel{24} \: \: \: \: \: \: \: \: \: \: \: \\ \\ : \implies \: area = 60 \times 12 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ : \implies \: area = 720 \: cm^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

hence, area of trapezium PQRS is 720cm² ✔︎

☆ trapezium →

・A trapezium is a quadrilateral having a pair of parallel sides

• Sum of all four angles of the trapezium is equal to 360°
• A trapezium has two parallel sides and two non-parallel sides.
• diagonals of regular trapezium bisect each other

Answer 2

$\underline{\underline{\sf{\maltese\:\:Question}}}$

• 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.

$\underline{\underline{\sf{\maltese\:\:Given}}}$

• PQRS is a trapezium

• PS ∥ QR

• QP⊥PS

• PS = 25 cm

• QR = 35 cm

• PQ = 24 cm

$\underline{\underline{\sf{\maltese\:\:To\:Find}}}$

• Area of the trapezium PQRS

$\underline{\underline{\sf{\maltese\:\:Answer}}}$

• Area of Trapezium PQRS = 720 cm²

$\underline{\underline{\sf{\maltese\:\:Calculations}}}$

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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