  Answer the following questions.
1) Find the area and perimeter of the shape with the given dimensions.
A right triangle with base 3 cm and height 4 cm (Hint: Find the hypotenuse using the Pythagorean Theorem.)

 = 

 = 


a. 6 cm2
b. 12 cm2
c. 60 cm3
d. 12 cm
e. 30 cm

To solve this problem, we need to find both the area and the perimeter of a right triangle with a base of 3 cm and a height of 4 cm. Let's go step by step:

### 1. Finding the Area of the Triangle
The area (\(A\)) of a right triangle can be found using the formula:

\[
A = \frac{1}{2} \times \text{base} \times \text{height}
\]

Substituting the given values:

\[
A = \frac{1}{2} \times 3 \, \text{cm} \times 4 \, \text{cm} = 6 \, \text{cm}^2
\]

### 2. Finding the Hypotenuse
To find the hypotenuse (\(c\)), we use the Pythagorean Theorem:

\[
c = \sqrt{\text{base}^2 + \text{height}^2} = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \, \text{cm}
\]

### 3. Finding the Perimeter
The perimeter (\(P\)) of the triangle is the sum of all its sides:

\[
P = \text{base} + \text{height} + \text{hypotenuse} = 3 \, \text{cm} + 4 \, \text{cm} + 5 \, \text{cm} = 12 \, \text{cm}
\]

### Answers:
- **Area = 6 cm²** (Option a)
- **Perimeter = 12 cm** (Option d)

Thus, the correct answers are:

- Area: **a. 6 cm²**
- Perimeter: **d. 12 cm**

Would you like more details or have any questions? Here are some related questions:

1. How do you calculate the area of other types of triangles, like equilateral or isosceles?
2. What is the relationship between the sides of a right triangle?
3. How do you calculate the area of a circle?
4. How do you find the perimeter of different geometric shapes, such as rectangles or circles?
5. What is the significance of the Pythagorean Theorem in geometry?

**Tip:** Always double-check the units for each part of your calculations to ensure they are consistent throughout the problem.

Answer the following questions. 1) Find the area and perimeter of the shape with the given dimensions. A right triangle with base 3 cm and height 4 cm (Hint: Find the hypotenuse using the Pythagorean Theorem.)

Learn how to find the area and perimeter of a right triangle with a base of 3 cm and a height of 4 cm. This problem involves using key geometric formulas, including the area formula for a triangle and the Pythagorean Theorem. Suitable for students in Grades 6-8.

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