Question

solve question 8 its urgent​

Answer 1

Given :

• DEFG is a trapezium.
• DE = 25cm
• GF = 11 cm .
• Area of ∆FTE is 84 cm².

To Find :

The area of the trapezium.

Solution :

Analysis :

Here we first have to find the height of the triangle from the area and the given dimensions. Then considering the height of the triangle as the distance between the two parallel sides of the trapezium we can find the area.

Required Formula :

• Area of triangle = ½ × base × height

• Area of trapezium = ½ × (a + b) × d

where,

• a & b = parallel sides
• d = distance between them

Explanation :

Area of triangle :

We know that,

DE = 25 cm & GF = 11 cm

• DT = GF = 11 cm (∵ GFTD forms a parallelogram and opposite sides of parallelogram are same)

So,

⇒ DT + TE = DE

⇒ 11 + TE = 25

⇒ TE = 25 - 11

∴ TE = 14 cm.

• The base of the triangle is 14 cm.

Let the height of the triangle be “h cm”.

We know that if we are given the area and base of the triangle and is asked to find the height of the triangle then our required formula is,

Area of triangle = ½ × base × height

where,

• Base = 14 cm
• Area = 84 cm²
• Height = h cm

Using the required formula and substituting the required values,

⇒ Area of triangle = ½ × base × height

⇒ 84 = ½ × 14 × h

⇒ 84 = 1 × 7 × h

⇒ 84/7 = h

⇒ 12 = h

∴ Height = 12 cm.

Height of the triangle is 12 cm.

Area of trapezium :

Distance between the parallel sides of the trapezium DEFG is 12 cm.

We know that if we are given the two parallel sides of the trapezium and distance between them and is asked to find the height of the triangle then our required formula is,

Area of trapezium = ½ × (a + b) × d

where,

• a = 11 cm
• b = 25 cm
• d = 12 cm

Using the required formula and substituting the required values,

⇒ Area of trapezium = ½ × (a + b) × d

⇒ Area = ½ × (11 + 25) × 12

⇒ Area = 1 × (11 + 25) × 6

⇒ Area = (36) × 6

⇒ Area = 36 × 6

⇒ Area = 216

∴ Area of trapezium = 216 cm².

The area of the trapezium DEFG is 216 cm².