Mastering Triangle Area Calculations for the CAASPP Math Exam

If a triangle has a height of 5 cm and a base of 10 cm, what is its area?

• A. 15 cm²
• B. 25 cm²
• C. 30 cm²
• D. 40 cm²

Answer: (B)

To find the area of a triangle, the formula used is: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \] In this case, the base is 10 cm and the height is 5 cm. Plugging these values into the formula: \[ \text{Area} = \frac{1}{2} \times 10 \text{ cm} \times 5 \text{ cm} \] Calculating it step by step: 1. Multiply the base by the height: \( 10 \text{ cm} \times 5 \text{ cm} = 50 \text{ cm}^2 \) 2. Now, take half of that result: \( \frac{1}{2} \times 50 \text{ cm}^2 = 25 \text{ cm}^2 \) Thus, the area of the triangle is correctly calculated to be 25 cm². This aligns with the answer provided, showing a clear grasp of how to apply the area formula for triangles.

Understanding how to calculate the area of a triangle is perhaps one of those essential skills that can genuinely pave the way for your success in the CAASPP Math Exam. You know what? Geometry isn’t just about working with shapes; it’s about unlocking your potential!

So, let’s tackle an example step by step: If a triangle has a height of 5 cm and a base of 10 cm, what's the area? Before you start guessing, let’s recall the formula:

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

Plugging in our values—from your trusty triangle toolkit—gives us:

[ \text{Area} = \frac{1}{2} \times 10 \text{ cm} \times 5 \text{ cm} ]

Okay, let’s break it down. First, multiply the base (10 cm) by the height (5 cm). What do we get?

[ 10 \text{ cm} \times 5 \text{ cm} = 50 \text{ cm}^2 ]

Now, here’s the tricky yet satisfying part: we take half of 50 cm². Why half? That’s how triangles work, right?

[ \frac{1}{2} \times 50 \text{ cm}^2 = 25 \text{ cm}^2 ]

Boom! The area of our triangle becomes 25 cm². If you thought that was easy, keep reading! Calculating the area of a triangle is not just about numbers—it's about building confidence.

You see, mastering such concepts prepares you not just for the CAASPP, but also for a world where you'll continuously encounter similar shapes and measurements. Think about it: whether you’re designing your dream garden or determining how much paint you need for the walls, knowing how to calculate area comes in handy!

But let’s not forget: the CAASPP Math Exam tests more than just straightforward calculations. It pushes you to apply these concepts practically. Communicating your reasoning or showing your work carries weight too! As you study, practice explaining your thought process. Wouldn’t that feel good?

In conclusion, mastering the area of triangles is a fantastic step toward acing your CAASPP Math Exam. Every small victory counts. Keep practicing, and soon you'll find yourself confidently solving similar problems! Whether you're cracking a challenging question or strolling through math concepts, remember that every challenge is just a stepping stone to your success!