Area of Isosceles Triangles Worksheets - Free Printable

Let’s solve each problem step by step.

We are given isosceles triangles and need to find their areas.
In an isosceles triangle, the altitude drawn from the top vertex to the base splits the base into two equal parts and forms two right triangles. We can use the Pythagorean theorem to find the height if it’s not given.

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

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Problem 1:

Triangle with sides: 14 ft, 14 ft, base = 12 ft

Step 1: Split base in half → 12 ÷ 2 = 6 ft
Step 2: Use Pythagoras to find height:
h² + 6² = 14²
h² + 36 = 196
h² = 160
h = √160 ≈ 12.649 ft

Step 3: Area = (12 × 12.649) ÷ 2 ≈ 151.788 ÷ 2 ≈ 75.9 ft²

Wait — let me double-check that calculation.

Actually, √160 = √(16×10) = 4√10 ≈ 4×3.162 = 12.648 → correct.

12 × 12.648 = 151.776 → divided by 2 = 75.888 → rounded to one decimal place = 75.9

✔ Correct.

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Problem 2:

Triangle with sides: 12 in, 12 in, base = 8 in

Step 1: Half base = 8 ÷ 2 = 4 in
Step 2: h² + 4² = 12² → h² + 16 = 144 → h² = 128 → h = √128 ≈ 11.314 in

Step 3: Area = (8 × 11.314) ÷ 2 = 90.512 ÷ 2 = 45.256 → 45.3 in²

Check: √128 = √(64×2) = 8√2 ≈ 8×1.414 = 11.312 → close enough.

8 × 11.312 = 90.496 → ÷2 = 45.248 → rounds to 45.2? Wait — let's be precise.

Actually, 8√2 = 11.3137...
8 × 11.3137 = 90.5096 → ÷2 = 45.2548 → rounds to 45.3

Yes, because 0.2548 is closer to 0.3 than 0.2? No — rounding rules: look at hundredths digit.

45.2548 → tenths digit is 2, hundredths is 5 → round up → 45.3

✔ So 45.3 in²

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Problem 3:

Sides: 20 cm, 20 cm, base = 10 cm

Half base = 5 cm
h² + 5² = 20² → h² + 25 = 400 → h² = 375 → h = √375

√375 = √(25×15) = 5√15 ≈ 5×3.873 = 19.365 cm

Area = (10 × 19.365) ÷ 2 = 193.65 ÷ 2 = 96.825 → 96.8 cm²

Check: 5√15 ≈ 5×3.87298 = 19.3649 → same.

10 × 19.3649 = 193.649 → ÷2 = 96.8245 → rounds to 96.8

✔ Correct.

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Problem 4:

Sides: 14 m, 14 m, base = 10 m

Half base = 5 m
h² + 5² = 14² → h² + 25 = 196 → h² = 171 → h = √171

√171 ≈ ? Let’s calculate: 13²=169, so √171 ≈ 13.0767

Area = (10 × 13.0767) ÷ 2 = 130.767 ÷ 2 = 65.3835 → 65.4 m²

Check: 13.0767 × 10 = 130.767 → ÷2 = 65.3835 → rounds to 65.4

✔ Correct.

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Problem 5:

Sides: 12 mm, 12 mm, base = 10 mm

Half base = 5 mm
h² + 5² = 12² → h² + 25 = 144 → h² = 119 → h = √119

√119 ≈ 10.9087

Area = (10 × 10.9087) ÷ 2 = 109.087 ÷ 2 = 54.5435 → 54.5 mm²

Check: 10.9087 × 10 = 109.087 → ÷2 = 54.5435 → rounds to 54.5

✔ Correct.

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Problem 6:

Sides: 13 in, 13 in, base = 10 in

Half base = 5 in
h² + 5² = 13² → h² + 25 = 169 → h² = 144 → h = 12 in (exact!)

Area = (10 × 12) ÷ 2 = 120 ÷ 2 = 60.0 in²

✔ Exact value — no rounding needed.

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Problem 7:

Sides: 10 yd, 10 yd, base = 12 yd

Half base = 6 yd
h² + 6² = 10² → h² + 36 = 100 → h² = 64 → h = 8 yd (exact!)

Area = (12 × 8) ÷ 2 = 96 ÷ 2 = 48.0 yd²

✔ Exact.

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Problem 8:

Sides: 15 cm, 15 cm, base = 12 cm

Half base = 6 cm
h² + 6² = 15² → h² + 36 = 225 → h² = 189 → h = √189

√189 = √(9×21) = 3√21 ≈ 3×4.5826 = 13.7478 cm

Area = (12 × 13.7478) ÷ 2 = 164.9736 ÷ 2 = 82.4868 → 82.5 cm²

Check: 13.7478 × 12 = 164.9736 → ÷2 = 82.4868 → rounds to 82.5

✔ Correct.

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Problem 9:

Sides: 8 in, 8 in, base = 6 in

Half base = 3 in
h² + 3² = 8² → h² + 9 = 64 → h² = 55 → h = √55 ≈ 7.4162 in

Area = (6 × 7.4162) ÷ 2 = 44.4972 ÷ 2 = 22.2486 → 22.2 in²

Check: 7.4162 × 6 = 44.4972 → ÷2 = 22.2486 → rounds to 22.2

✔ Correct.

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Now let’s list all answers clearly:

1) 75.9 ft²
2) 45.3 in²
3) 96.8 cm²
4) 65.4 m²
5) 54.5 mm²
6) 60.0 in²
7) 48.0 yd²
8) 82.5 cm²
9) 22.2 in²

Final Answer:
1) 75.9
2) 45.3
3) 96.8
4) 65.4
5) 54.5
6) 60.0
7) 48.0
8) 82.5
9) 22.2