Subjects geometry

Triangle Area 85C7Fa

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Question: Note: Not all assigned work was completed prior to the Topic Test. So this question could be unfamiliar. 19.6 mm 24.1 mm 23.4 mm 22.7 mm The area of the triangle is ____ mm². Graph/shape description: A triangle is shown in the top-left; the left side is labeled 19.6 mm, the right side is labeled 24.1 mm, the base is labeled 22.7 mm, and a dashed segment from the left side to the bottom-right vertex is labeled 23.4 mm with a right-angle marker where it meets the left side.
1. **State the problem:** We need to find the area of a triangle with sides labeled as follows: left side = $19.6$ mm, right side = $24.1$ mm, base = $22.7$ mm, and a dashed segment (height) = $23.4$ mm perpendicular to the left side. 2. **Formula for the area of a triangle:** The area $A$ can be found using the formula: $$A = \frac{1}{2} \times \text{base} \times \text{height}$$ 3. **Identify base and height:** Here, the base is given as $22.7$ mm, and the height (perpendicular segment) is $23.4$ mm. 4. **Calculate the area:** Substitute the values into the formula: $$A = \frac{1}{2} \times 22.7 \times 23.4$$ 5. **Intermediate calculation:** $$A = \frac{1}{2} \times 531.18$$ 6. **Simplify:** $$A = 265.59$$ 7. **Final answer:** The area of the triangle is $265.59$ mm².
19.6 mm22.7 mm24.1 mm23.4 mm