Question

find the area of the trapezium in the image​

Answer 1

Given

• Trapezium EFGH
• EH → 23 cm
• FG → 35 cm
• EG → 37 cm
• EH ll FG
• EF ⊥ GF

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To Find

• The area of the trapezium

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Solution

We'll first find the height of the trapezium. If we look closely we can find a right-angled triangle in the given trapezium. So, using the Pythagorean Theorem we will find the height.

Pythagorean Theorem → (Base)² + (Height)² = (Hypotenuse)²

Base → 35 cm

Height → x cm

Hypotenuse → 37 cm

Let's find the height step-by-step.

(35)² + (x)² = (37)²

Step 1: Simplify the equation.

→ (35)² + (x)² = (37)²

→ 1225 + x² = 1369

Step 2: Subtract 1225 from both sides of the equation.

→ 1225 + x² - 1225 = 1369 - 1225

→ x² = 144

Step 3: Find the square root of 144

→ x = √144

→ x = 12

∴ The height of the trapezium is 12 cm

With the obtained value of the height of the trapezium, we'll find the area of the trapezium.

Formula to find the Area of Trapezium → $\sf \dfrac{Side_{1} + Side_{2}}{2}\times Height$

Side₁ → 23 cm

Side₂ → 35 cm

Height → 12 cm

↦ $\sf \dfrac{23+35}{2}\times 12$

↦ $\sf \dfrac{58}{2}\times 12$

↦ $\sf 29 \times 12$

↦ $\sf 348 \ cm^{2}$

∴ The area of the following trapezium is 348 cm²

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Answer 2

Step-by-step explanation:

Given

Trapezium EFGH

EH → 23 cm

FG → 35 cm

EG → 37 cm

EH ll FG

EF ⊥ GF

_______________________________________

To Find

The area of the trapezium

_______________________________________

Solution

We'll first find the height of the trapezium. If we look closely we can find a right-angled triangle in the given trapezium. So, using the Pythagorean Theorem we will find the height.

Pythagorean Theorem → (Base)² + (Height)² = (Hypotenuse)²

Base → 35 cm

Height → x cm

Hypotenuse → 37 cm

Let's find the height step-by-step.

(35)² + (x)² = (37)²

Step 1: Simplify the equation.

→ (35)² + (x)² = (37)²

→ 1225 + x² = 1369

Step 2: Subtract 1225 from both sides of the equation.

→ 1225 + x² - 1225 = 1369 - 1225

→ x² = 144

Step 3: Find the square root of 144

→ x = √144

→ x = 12

∴ The height of the trapezium is 12 cm

With the obtained value of the height of the trapezium, we'll find the area of the trapezium.

Formula to find the Area of Trapezium →

Side₁ +Side₂/2 ×height

Side₁ → 23 cm

Side₂ → 35 cm

Height → 12 cm

=23+35/2 ×12

= 58/2×12

= 29×12

=348 cm²

∴ The area of the following trapezium is 348 cm²