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

Or approximate:
$$
s^2 = 34.81 \\
\frac{\sqrt{3}}{4} \approx 0.433 \\
0.433 \times 34.81 \approx 15.08
$$

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

✔ Type: Equilateral

> ✔ Answer:
- Area: 15.08 yd²
- Perimeter: 17.7 yd
- 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

Diagram shows two sides labeled b, so it's isosceles with two equal sides b

So:
- Two equal sides: b = 6.4 cm
- Base: a = 4.5 cm

We need height to find area, but not given. However, since it's isosceles, we can compute height using Pythagoras.

Split base into two: 4.5 / 2 = 2.25 cm

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

✔ Area:
$$
\frac{1}{2} \times a \times h = \frac{1}{2} \times 4.5 \times 5.99 \approx 0.5 \times 26.955 = \boxed{13.48} \text{ cm}^2
$$

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

✔ Type: Isosceles

> ✔ 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

Right triangle? Diagram shows right angle at c, so right angle between a and b?

Wait — label h is drawn from vertex to side c, and there’s a right angle symbol at c — so angle C is 90°, so a and b are legs, c is hypotenuse.

Yes — right triangle.

✔ Area:
$$
\frac{1}{2} \times a \times b = \frac{1}{2} \times 6.33 \times 8.16 = 0.5 \times 51.5408 = \boxed{25.77} \text{ yd}^2
$$

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

✔ Type: Right triangle

> ✔ Answer:
- Area: 25.77 yd²
- Perimeter: 23.09 yd
- Type: Right triangle

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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

Diagram shows two sides labeled b, so two equal sides = 6.7 inches, base = 4 inches

So isosceles triangle

Need height to find area.

Split base: 4 / 2 = 2 inches

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

✔ 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 yd | Equilateral |
| 5 | 18.49 ft² | 22.52 ft | Right |
| 6 | 13.48 cm² | 17.3 cm | Isosceles |
| 7 | 25.77 yd² | 23.09 yd | Right |
| 8 | 20.5 cm² | 22.8 cm | Right |
| 9 | 12.8 in² | 17.4 in | Isosceles |

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