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Title: Triangles

Grade: 8-a Lesson: S2-L5

Explanation: Let us verify the answer here with the steps.

Description:

Explanation	Answer
Problem	Find the area of an equilateral triangle that has sides equal to 40 cm.
Formula used	\$"Area of Triangle" = (1/2) \times "base" \times "height"\$
Step - 1	Side of a equilateral triangle = \$40 cm\$
Step - 2	By using the formula, \$("hypotenuse")^2 = ("side")^2 + ("side")^2\$ \$(40)^2 = h^2 + (20)^2\$ ⇒ \$1600 = h^2 + 400\$ ⇒ \$1600 - 400 = h^2 \$ ⇒ \$h^2 = 1200\$ ⇒ \$h = \sqrt1200 = 34.64\$
Step - 3	\$"Area of Triangle" = (1/2) \times "base" \times "height"\$ ⇒ \$"Area of Triangle" = (1/\cancel2^1) \times \cancel40^20 \times 34.64\$ ⇒ \$"Area of Triangle" = 20 \times 34.64 = 69.28\$
Step - 4	Therefore, the area of an equilateral triangle is 69.28 cm

Explanation

Answer

Problem

Find the area of an equilateral triangle that has sides equal to 40 cm.

Formula used

\$"Area of Triangle" = (1/2) \times "base" \times "height"\$

Step - 1

Side of a equilateral triangle = \$40 cm\$

Step - 2

By using the formula,

\$("hypotenuse")^2 = ("side")^2 + ("side")^2\$

\$(40)^2 = h^2 + (20)^2\$

⇒ \$1600 = h^2 + 400\$

⇒ \$1600 - 400 = h^2 \$

⇒ \$h^2 = 1200\$

⇒ \$h = \sqrt1200 = 34.64\$

Step - 3

\$"Area of Triangle" = (1/2) \times "base" \times "height"\$

⇒ \$"Area of Triangle" = (1/\cancel2^1) \times \cancel40^20 \times 34.64\$

⇒ \$"Area of Triangle" = 20 \times 34.64 = 69.28\$

Step - 4

Therefore, the area of an equilateral triangle is 69.28 cm