Geometry Worksheets | Triangle Worksheets - Free Printable

Let's solve each triangle problem step by step. We will calculate the Area, Perimeter, and identify the Type of each triangle.

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🔷 Formulas Used:

- Area of a Triangle:
$$
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
$$

- Perimeter of a Triangle:
$$
\text{Perimeter} = a + b + c
$$

- Triangle Types:
- Right triangle: One angle is 90° (indicated by a square corner).
- Equilateral: All sides equal.
- Isosceles: Two sides equal.
- Scalene: All sides different.
- Acute/Obtuse: Based on angles, but we can infer from side lengths if needed.

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Let’s go through each one:

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1)

Given:
- a = 4.27 ft
- b = 8.21 ft
- c = 9.8 ft
- h = 4 ft

Assuming h is the height corresponding to base b (since it's drawn from vertex opposite side c), or maybe to side a? But in diagram, h is perpendicular to side c, so likely base = c, height = h.

But wait: in diagram, the right angle is between a and b, so this is a right triangle with legs a and b, hypotenuse c.

So:
- Base = a = 4.27 ft
- Height = b = 8.21 ft
- Or vice versa — doesn't matter for area.

✔ Area:
$$
\text{Area} = \frac{1}{2} \times a \times b = \frac{1}{2} \times 4.27 \times 8.21
= 0.5 \times 34.9667 = 17.48335 \approx \boxed{17.48} \text{ ft}^2
$$

✔ Perimeter:
$$
P = a + b + c = 4.27 + 8.21 + 9.8 = \boxed{22.28} \text{ ft}
$$

✔ Type: Right triangle (has right angle)

> ✔ Answer:
- Area: 17.48 ft²
- Perimeter: 22.28 ft
- Type: Right triangle

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2)

Given:
- a = 7.4 inches
- b = 4.8 inches
- c = 8.82 inches

Right triangle (right angle at bottom left, between a and b).

So:
- Legs: a and b → use for area
- Hypotenuse: c

✔ Area:
$$
\frac{1}{2} \times a \times b = \frac{1}{2} \times 7.4 \times 4.8 = 0.5 \times 35.52 = \boxed{17.76} \text{ in}^2
$$

✔ Perimeter:
$$
7.4 + 4.8 + 8.82 = \boxed{21.02} \text{ in}
$$

✔ Type: Right triangle

> ✔ Answer:
- Area: 17.76 in²
- Perimeter: 21.02 in
- Type: Right triangle

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3)

Given:
- a = 5.71 mm
- b = 8.49 mm
- c = 8.4 mm
- h = 5.4 mm

From diagram: h is drawn from vertex to side c, so base = c, height = h

✔ Area:
$$
\frac{1}{2} \times c \times h = \frac{1}{2} \times 8.4 \times 5.4 = 0.5 \times 45.36 = \boxed{22.68} \text{ mm}^2
$$

✔ Perimeter:
$$
5.71 + 8.49 + 8.4 = \boxed{22.6} \text{ mm}
$$

✔ Type: Sides are all different → scalene

> ✔ Answer:
- Area: 22.68 mm²
- Perimeter: 22.6 mm
- Type: Scalene

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4)

Given:
- s = 5.9 yds (all sides equal)

This is an equilateral triangle

✔ Area:
Use formula:
$$
\text{Area} = \frac{\sqrt{3}}{4} \times s^2 = \frac{1.732}{4} \times (5.9)^2
= 0.433 \times 34.81 \approx \boxed{15.08} \text{ yd}^2
$$

Or more accurately:
$$
\frac{\sqrt{3}}{4} \times 34.81 \approx \frac{1.73205}{4} \times 34.81 \approx 0.43301 \times 34.81 \approx 15.08 \text{ yd}^2
$$

✔ Perimeter:
$$
3 \times 5.9 = \boxed{17.7} \text{ yds}
$$

✔ Type: Equilateral

> ✔ Answer:
- Area: 15.08 yd²
- Perimeter: 17.7 yds
- Type: Equilateral

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5)

Given:
- a = 8.6 ft
- b = 4.3 ft
- c = 9.62 ft

Right triangle (right angle between a and b)

✔ Area:
$$
\frac{1}{2} \times a \times b = \frac{1}{2} \times 8.6 \times 4.3 = 0.5 \times 36.98 = \boxed{18.49} \text{ ft}^2
$$

✔ Perimeter:
$$
8.6 + 4.3 + 9.62 = \boxed{22.52} \text{ ft}
$$

✔ Type: Right triangle

> ✔ Answer:
- Area: 18.49 ft²
- Perimeter: 22.52 ft
- Type: Right triangle

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6)

Given:
- a = 4.5 cm
- b = 6.4 cm
- No height given

From diagram: two sides labeled b, so isosceles triangle with two equal sides.

Wait: b = 6.4 cm, and a = 4.5 cm. So two equal sides are b, meaning both sides from top are 6.4 cm, base is a = 4.5 cm

But no height given.

We cannot compute area without height unless we assume it's not a right triangle.

But there's no right angle shown, so we cannot use Pythagoras directly.

Wait — but perhaps we can use the formula for isosceles triangle?

But we need height.

Alternatively, maybe we’re supposed to use the given values as they are.

But no height is given.

Wait — look again: only a = 4.5 cm, b = 6.4 cm, and no h.

But the triangle has two sides labeled b, so it's isosceles with two equal sides of 6.4 cm, base 4.5 cm

To find area, we need height from apex to base.

Let’s compute height using Pythagoras.

Split base into two: $ \frac{4.5}{2} = 2.25 $ cm

Then:
$$
h = \sqrt{b^2 - (a/2)^2} = \sqrt{6.4^2 - 2.25^2} = \sqrt{40.96 - 5.0625} = \sqrt{35.8975} \approx 5.99 \text{ cm}
$$

Now,
✔ Area:
$$
\frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 4.5 \times 5.99 \approx 0.5 \times 26.955 = \boxed{13.48} \text{ cm}^2
$$

✔ Perimeter:
$$
6.4 + 6.4 + 4.5 = \boxed{17.3} \text{ cm}
$$

✔ Type: Isosceles (two equal sides)

> ✔ Answer:
- Area: 13.48 cm²
- Perimeter: 17.3 cm
- Type: Isosceles

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7)

Given:
- a = 6.33 yds
- b = 8.16 yds
- c = 8.6 yds
- h = 5.7 yds

From diagram: h is drawn to side c, so base = c, height = h

✔ Area:
$$
\frac{1}{2} \times c \times h = \frac{1}{2} \times 8.6 \times 5.7 = 0.5 \times 49.02 = \boxed{24.51} \text{ yd}^2
$$

✔ Perimeter:
$$
6.33 + 8.16 + 8.6 = \boxed{23.09} \text{ yds}
$$

✔ Type: All sides different → scalene

> ✔ Answer:
- Area: 24.51 yd²
- Perimeter: 23.09 yds
- Type: Scalene

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8)

Given:
- a = 8.2 cm
- b = 5 cm
- c = 9.6 cm

Right triangle (right angle between a and b)

✔ Area:
$$
\frac{1}{2} \times a \times b = \frac{1}{2} \times 8.2 \times 5 = 0.5 \times 41 = \boxed{20.5} \text{ cm}^2
$$

✔ Perimeter:
$$
8.2 + 5 + 9.6 = \boxed{22.8} \text{ cm}
$$

✔ Type: Right triangle

> ✔ Answer:
- Area: 20.5 cm²
- Perimeter: 22.8 cm
- Type: Right triangle

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9)

Given:
- a = 4 inches
- b = 6.7 inches

From diagram: two sides labeled b, so isosceles triangle with two equal sides of 6.7 inches, base = a = 4 inches

No height given, so compute it.

Split base: $ \frac{4}{2} = 2 $ inches

Height:
$$
h = \sqrt{6.7^2 - 2^2} = \sqrt{44.89 - 4} = \sqrt{40.89} \approx 6.4 \text{ inches}
$$

✔ Area:
$$
\frac{1}{2} \times 4 \times 6.4 = 2 \times 6.4 = \boxed{12.8} \text{ in}^2
$$

✔ Perimeter:
$$
6.7 + 6.7 + 4 = \boxed{17.4} \text{ in}
$$

✔ Type: Isosceles

> ✔ Answer:
- Area: 12.8 in²
- Perimeter: 17.4 in
- Type: Isosceles

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✔ Final Answers Summary:

| # | Area | Perimeter | Type |
|---|------|-----------|------|
| 1 | 17.48 ft² | 22.28 ft | Right |
| 2 | 17.76 in² | 21.02 in | Right |
| 3 | 22.68 mm² | 22.6 mm | Scalene |
| 4 | 15.08 yd² | 17.7 yds | Equilateral |
| 5 | 18.49 ft² | 22.52 ft | Right |
| 6 | 13.48 cm² | 17.3 cm | Isosceles |
| 7 | 24.51 yd² | 23.09 yds | Scalene |
| 8 | 20.5 cm² | 22.8 cm | Right |
| 9 | 12.8 in² | 17.4 in | Isosceles |

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Let me know if you'd like these filled out in the worksheet format!