Question

Each side of an equilateral triange measures 8cm
Find (a) the area of the triangle correct to 2 place of decimal and
(b) the height oF the triangle correct to 2 place of decimal

Answer 1

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✺Answer:

♦️GiveN:

• Side of an equilateral triangle = 8cm

♦️To FinD:

• Area of the traingle correct upto 2 decimal places.
• Height of the traingle.

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✺Explanation of Q.

The above question is simple and based on "Apply formula and get solution". Side of equilateral triangle is given 8 cm, and we can find area by using formula:

$\large {\star{ \boxed{ \rm{ \purple{Area \: of \: eq. \: \triangle = \frac{ \sqrt{3} }{4} \times {a}^{2} }}}}}$

❄Note:

Where, a = side of eq. triangle

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This formula was derived from the heron's formula i.e.

$\large{\star{ \boxed{ \rm{ \red{Area \: of \: any \: \triangle = \sqrt{s(s - a)(s - b)(s - c)}}}}}}$

Where, a,b,c are the sides of the triangle and S is the semiperemeter. In equilateral triangle a=b=c So, by deriving we will get simplified formula for area of equilateral triangle.

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We also known, a other formula for area of triangle when the height and the corresponding base are given i.e.

$\large{\star{ \boxed{ \green{ \rm{ Area \: of \: \triangle = \frac{1}{2} \times h \times b}}}}}$

We know all the sides of equilateral traingle is equal ,so we can find the height if area and base is known.

By using the above formuale,we will solve both the questions.

↪ Refer to the attachment.....

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✺Solution:

a) Side of equilateral triangle = 8 cm

By using formula,

$\large{ \rm{ \rightarrow \: Area \: of \: eq. \: \triangle = \frac{ \sqrt{3} }{4} \times {8}^{2} \: {cm}^{2} }} \\ \\ \large{ \rm{ \rightarrow \: Area \: of \: eq. \: \triangle = \frac{ \sqrt{3} }{4} \times 64 \: {cm}^{2} }} \\ \\ \large{ \rm{ \rightarrow \: Area \: of \: eq. \: \triangle = 16 \sqrt{3} {cm}^{2} }} \\ \\ \large{ \rm{ \rightarrow \: Area \: of \: eq. \: \triangle \approx \: \boxed{ \red{27.712\: {cm}^{2} }}}}\\ \\ \large{\rm{\therefore{\underline{\purple{Area\: of \:equilateral \: triangle = 27.712 cm^2}}}}}$

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b) Our base is 8 cm, and area = 27. 712 cm^2

Now we can find the height by using formula.

By using formula,

$\large{ \rm{ \rightarrow \: \frac{1}{2} \times h \times 8 = 27.712 \: {cm}^{2} }} \\ \\ \large{ \rm{ \rightarrow \: h = \cancel{ \frac{27.712 \: \times 2}{8} \: cm}}} \\ \\ \large{ \rm{ \rightarrow \: h \approx \boxed{ \rm{ \red{6.928 \: cm}}}}} \\ \\ \large{\rm{\therefore{\underline{\purple{Height \:of \:equilateral \: triangle= 6.928 \:cm}}}}}$

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