Question

A trapezium has parallel sides : 10m and 25m, non-parallel sides : 13m and 14m. The height of the trapezium is

Answer 1

Solution :-

( Refer to Image First .)

From image we have :-

→ AB = 10m. (Given).

→ DC = 25m . (Given).

→ AD = 14m. (Given).

→ BC = 13m. (Given).

Construction :-

→ Draw AE & BF that are Perpendicular to DC.

now,

→ Let DE = x m.

→ EF = AB = 10m

→ FC = 25 - (10 + x)

→ FC = (15 - x) m.

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Than, in Right ∆AED, we have ,

→ AE² = AD² - DE² (By Pythagoras Theoram)

→ AE² = (14)² - (x)² ------ Equation (1).

Similarly,

in Right ∆BFC, we have ,

→ BF² = BC² - FC² (By Pythagoras Theoram)

→ AE² = (13)² - (15-x)² ------ Equation (2).

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Since, AE = BF ( Height of Trapezium.)

Comparing Both Equations we get ,

→ (14)² - x² = (13)² - (15 - x)²

→ 196 - x² = 169 - (225 + x² - 30x)

→ 196 - x² = 169 - 225 - x² + 30x

→ 30x = 196 + 225 - 169

→ 30x = 252

→ x = 8.4 m.

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Therefore,

→ AE² = (14)² - x²

→ AE² = (14)² - (8.4)²

→ AE² = (14+8.4)(14 - 8.4)

→ AE² = 22.4 * 5.6

→ AE² = 4 * 5.6 * 5.6

→ AE² = 2² * 5.6²

→ AE² = (2*5.6)²

→ AE = 2*5.6

→ AE = 11.2 m. (Ans.)

Hence, Height of Trapezium is 11.2m.

Answer 2

Step-by-step explanation:

$\bf \huge \: Question \: \: \:$

A trapezium has parallel sides : 10m and 25m, non-parallel sides : 13m and 14m. The height of the trapezium is

___________________________

$\bf \huge \: Given \: \: \:$

• A trapezium has parallel sides :

• 10m and 25m, non-parallel sides : 13m and 14m.

___________________________

$\bf \huge \: To \: Find\: \:$

supposed :-

The ABCD be a trapezium with sides

• AB = 25 m,
• BC = 13 m,
• CD = 10 m
• DA = 14 m.

___________________________

We have parallel line from DE parallel to BC.

Side BC = 13 m

Then

DE = 13 m.

A new triangle ADE is constructed

• sides DA = 14 m,
• AE = 15 m
• DE = 13 m.

___________________________

s = (14 + 15 + 13)/2

s = 42/2

s = 21 m

Applying Heron's formula,:-

$\tt \sqrt{s} (s-a)(s-b)(s-c)$

putting all values :-

$\tt\sqrt{21} (21-14)(21-15)(21-13)$

$\tt\sqrt{21}  × 7 × 6 × 8$

$\tt\sqrt{ 7056}$

Area of the triangle ADE$\tt = 84 m^2$

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we have formula

Area ...of ...triangle$\tt =\frac{1}{2}  × base × height\:$

Putting all value;-

$\tt 84 =\frac{1}{2}× 15 × h\:$

$\tt 168 =15h\:$

$\tt H =\frac{168}{8}\:$

$\tt H = 11.2 m\:$

The height of the trapezium is 11 .2m

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