Area and Perimeter of Triangles - K12 Math Worksheets - Free Printable

Let’s solve each problem one by one.
We’re finding the area of equilateral triangles.
All sides are equal, and we’re given the height (the dotted line inside each triangle).

The formula for area of any triangle is:
> Area = (base × height) ÷ 2

Since these are equilateral triangles, the base is just the length of any side — and we’re told all sides are equal.

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Problem 1:
Base = 4 cm
Height = 3.464 cm
Area = (4 × 3.464) ÷ 2 = 13.856 ÷ 2 = 6.928 cm²

✔ Check: 4 × 3.464 = 13.856 → divided by 2 = 6.928 ✔️

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Problem 2:
Base = 21 ft
Height = 18.187 ft
Area = (21 × 18.187) ÷ 2
First, 21 × 18.187 = let’s calculate:
20 × 18.187 = 363.74
1 × 18.187 = 18.187
Total = 363.74 + 18.187 = 381.927
Now divide by 2: 381.927 ÷ 2 = 190.9635 ft²

✔ We can round to 3 decimal places if needed → 190.964 ft² (but since input had 3 decimals, keep as is or match precision)

Actually, let’s do exact multiplication:
21 × 18.187 =
Break it down:
18.187 × 20 = 363.74
18.187 × 1 = 18.187
Sum: 363.74 + 18.187 = 381.927
÷2 = 190.9635 → So 190.964 ft² (rounded to 3 decimals)

But maybe they expect exact value? Let’s see other problems — probably keep 3 decimals.

Wait — in problem 1, answer was 6.928 which is exact from 4×3.464/2.

Similarly here: 21 × 18.187 = 381.927 → /2 = 190.9635 → so perhaps write as 190.964 ft²

But let’s check with calculator-style:

21 * 18.187 = 381.927 → yes → /2 = 190.9635 → so 190.964 ft² (if rounding to 3 decimals)

Alternatively, maybe leave as 190.9635? But others have 3 decimals.

Looking at problem 3: 6 × 5.196 / 2 = 31.176 / 2 = 15.588 — that’s 3 decimals.

So for consistency, we’ll use 3 decimal places.

So Problem 2: 190.964 ft²

Wait — 190.9635 rounded to 3 decimals is 190.964 ✔️

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Problem 3:
Base = 6 in
Height = 5.196 in
Area = (6 × 5.196) ÷ 2 = 31.176 ÷ 2 = 15.588 in²

✔ Correct.

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Problem 4:
Base = 8 m
Height = 6.928 m
Area = (8 × 6.928) ÷ 2 = 55.424 ÷ 2 = 27.712 m²

✔ Correct.

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Problem 5:
Base = 12 cm
Height = 10.392 cm
Area = (12 × 10.392) ÷ 2 = 124.704 ÷ 2 = 62.352 cm²

✔ Correct.

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Problem 6:
Base = 8 in
Height = 6.928 in
This is same as Problem 4 but in inches.
Area = (8 × 6.928) ÷ 2 = 55.424 ÷ 2 = 27.712 in²

✔ Same calculation.

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Now, let’s list all answers clearly:

1) 6.928 cm²
2) 190.964 ft²
3) 15.588 in²
4) 27.712 m²
5) 62.352 cm²
6) 27.712 in²

Double-checking Problem 2 again because numbers are bigger:

21 × 18.187:

Let me compute 21 × 18 = 378
21 × 0.187 = ?

0.187 × 20 = 3.74
0.187 × 1 = 0.187
→ 3.74 + 0.187 = 3.927
So total = 378 + 3.927 = 381.927 → ÷2 = 190.9635 → rounds to 190.964

Yes.

All others are straightforward multiplications and divisions.

Final Answer:
1) 6.928 cm²
2) 190.964 ft²
3) 15.588 in²
4) 27.712 m²
5) 62.352 cm²
6) 27.712 in²