Question

The side of an equilateral triangle is 4√3 cm. Find it's area, base and
height.

Answer 1

♣ Qᴜᴇꜱᴛɪᴏɴ :

• The side of an equilateral triangle is 4√3 cm. Find it's area, base and altitude

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♣ ɢɪᴠᴇɴ :

• The side of an equilateral triangle is 4√3 cm

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♣ ᴛᴏ ꜰɪɴᴅ :

• Area, Base, Altitude of the following triangle :

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1, 0)(1,0)(3,3)\put(0, 1.6){ \bf }\qbezier(5,0)(5,0)(3,3)\put(5.0, 1.6){ \bf 4\sqrt{3}\ cm }\qbezier(5,0)(1,0)(1,0)\put(2.4, - 0.9){ \bf }\put(2.85,3.2){ \bf A }\put(0.5,-0.3){ \bf C }\put(5.2,-0.3){ \bf B }\end{picture}$

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♣ ᴄᴏɴᴄᴇᴘᴛ :

The concept is related to Triangles and their properties, and also finding area and perimeter of them. First note that we are asked to calculate area, base and altitude of an equilateral triangle

• An equilateral triangle has all sides equal.

• Area of an Equilateral Triangle = √3/4 (Side)²

• Altitude of Equilateral Triangle = √3/2 × Side

• Base of an equilateral triangle = Side

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♣ ᴀɴꜱᴡᴇʀ :

Area of Given Equilateral Triangle = 12√3 cm²

Altitude of Given Equilateral Triangle = 6 cm

Base of Given Equilateral Triangle = 4√3 cm

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♣ ᴄᴀʟᴄᴜʟᴀᴛɪᴏɴꜱ :

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1, 0)(1,0)(3,3)\put(0, 1.6){ \bf 4\sqrt{3}\ cm }\qbezier(5,0)(5,0)(3,3)\put(5.0, 1.6){ \bf 4\sqrt{3}\ cm }\qbezier(5,0)(1,0)(1,0)\put(2.4, - 0.9){ \bf 4\sqrt{3}\ cm }\put(2.85,3.2){ \bf A }\put(0.5,-0.3){ \bf C }\put(5.2,-0.3){ \bf B }\end{picture}$

First let's solve for area of the given equilateral triangle :

Area of an Equilateral Triangle = √3/4 (Side)²

Area of Given Equilateral Triangle

= √3/4 (Side)²

= √3/4 (4√3 cm)²

= √3/4 × 4√3 × 4√3 cm²

= √3/4 × 48 cm²

= 12√3 cm²

⭐ Area of Given Equilateral Triangle = 12√3 cm² ⭐

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Now solve for Altitude of the given equilateral triangle :

Altitude of Equilateral Triangle = √3/2 × Side

Altitude of Equilateral Triangle

= √3/2 × Side

= √3/2 × 4√3 cm

= 6 cm

⭐ Altitude of Given Equilateral Triangle = 6 cm ⭐

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Now solve for Base of the given equilateral triangle :

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1, 0)(1,0)(3,3)\put(0, 1.6){}\qbezier(5,0)(5,0)(3,3)\put(5.0, 1.6){}\qbezier(5,0)(1,0)(1,0)\put(2.1, - 0.9){ \bf 4\sqrt{3}\ cm \:\:(Bas{e}) }\put(2.85,3.2){ \bf A }\put(0.5,-0.3){ \bf C }\put(5.2,-0.3){ \bf B }\end{picture}$

Base of an equilateral triangle = Side

Base of an equilateral triangle

= Side

= 4√3 cm

⭐ Base of Given Equilateral Triangle = 4√3 cm ⭐

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❤️ Happy Learning ❤️

Answer 2

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