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Calculate the Area of a Triangle with Given Side and Corresponding Height
Mathematics
Grade 7 (Junior High School)
Question Content
Drag the yellow point until an accurate 'height' of the triangle is drawn. Afterwards, fill out the empty boxes below to determine the area of the triangle. The triangle has side lengths 6, 3.1, 6.6, and a given height h=3.39 corresponding to one of the sides.
Correct Answer
10.17
Detailed Solution Steps
1
Step 1: Identify the base corresponding to the given height. The dashed height h=3.39 is drawn perpendicular to the side with length 6, so this side is the base (b=6).
2
Step 2: Use the formula for the area of a triangle: Area = (1/2) × base × height.
3
Step 3: Substitute the values into the formula: Area = (1/2) × 6 × 3.39 = 3 × 3.39 = 10.17.
Knowledge Points Involved
1
Height of a Triangle
The height of a triangle is a perpendicular segment from a vertex to the opposite side (or its extension). It is used to calculate the area, and each side can act as a base with a corresponding unique height.
2
Area Formula for a Triangle
The formula is Area = (1/2) × b × h, where b is the length of the base (any side of the triangle) and h is the perpendicular height corresponding to that base. This formula comes from dividing a parallelogram (which has area base×height) into two congruent triangles.
3
Perpendicular Segments
A perpendicular segment forms a 90-degree (right) angle with the line it intersects. For triangle heights, this right angle ensures the measurement is the shortest vertical distance from the vertex to the base, which is required for the area formula to be valid.
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