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HUNTB-398 ### 1. Understand the Problem First, let's read the problem carefully: **Problem:** Let's clear up the problem. You are provided with a triangle formed by a 6cm side, another 6cm side, and a 5cm side. Your task is to find the area of this triangle. Additionally, a hint is given: The area can be determined by multiplying the base by the height and then dividing by two. Let's break this down: - You have a triangle with sides of lengths 6cm, 6cm, and 5cm. - You need to find the area of this triangle. ### 2. Visualize the Triangle Start by imagining or drawing the triangle. Since you have two sides both measuring 6cm, this suggests that there are two sides of equal length in the triangle. This means the triangle is **isosceles**. By having two equal sides, the triangle's base is likely the side measuring 5cm. Your triangle will look something like this: ``` A / / / B------C 5cm ``` Where sides AB and AC are both 6cm, and side BC is 5cm. ### 3. Hypothesis for Solving the Problem Given that the area is half of the product of the base and the height, you can follow these steps: 1. Find the "base" of the triangle. Given the sides, assume the base is the side with 5cm. 2. Find the "height" of the triangle by measuring the perpendicular distance from the base to the opposite vertex. 3. Multiply the base and the height, and then divide by two to find the area. However, you don't have the height directly. You'll need to find it using the lengths of the triangle. ### 4. Strategy for Finding the Height To find the height, consider an isosceles triangle. You can divide the triangle into two right triangles by drawing a perpendicular line from the apex to the base. This will make it easier to find the height. Here's how: ``` A / / / B------C 5cm ``` Divide the triangle into two right triangles by drawing a perpendicular line from point A to the base BC. Let's call the point where the perpendicular line meets the base point D. Now, you have two right triangles: ABD and ACD. ``` A / / / B------D----C ``` Given that BC is 5cm, the distance BD is half of that, which is 2.5cm. Since AB is 6cm, you can now think about the right triangle ABD to find the height. ### 5. Apply Pythagorean Theorem In the right triangle ABD, you can use the Pythagorean theorem to calculate the height AD. The Pythagorean theorem states: a² + b² = c² Here, c is the hypotenuse, which is AB (6cm), and b is the base (2.5cm). You're looking to find a, which is the height AD. So: a² + (2.5)² = 6² a² + 6.25 = 36 a² = 36 - 6.25 a² = 29.75 a = sqrt(29.75) a = 5.45cm (rounded to two decimal places) ### 6. Calculate the Area Now that you have the height, calculate the area: Area = (base * height) / 2 Area = (5cm * 5.45cm) / 2 Area = (27.25) / 2 Area = 13.625cm² ### 7. Conclusion The area of the triangle is **13.625cm²**. ### 8. Verification To verify, check if this aligns with the given hint: Area = (base * height) / 2 From the problem, base = 5cm and height = 5.45cm Area = (5 * 5.45) / 2 = 27.25 / 2 = 13.625cm² This confirms that the area is accurately determined. --- ### Answer: Area of the triangle is **13.625cm²**. ## Step-by-step explanation: 1. **Understand the Problem:** You have a triangle with sides of 6cm, 6cm, and 5cm. Find its area. 2. **Visualize the Triangle:** Draw an isosceles triangle with two sides of 6cm and a base of 5cm. 3. **Find the Height:** Split the triangle into two right triangles, and apply the Pythagorean theorem to find the height. 4. **Calculate the Area:** Using the formula, Area = (base * height) / 2, find the area. 5. **Verify:** Double-check the calculations to ensure accuracy. --- This method ensures that the area is accurately determined using the given sides of the triangle.

4 Nov 2022