Suppose that △𝑃𝑄𝑅 has an area of A square inches and that the vertices of △𝑆𝑇𝑈 are the midpoints of the sides of △𝑃𝑄𝑅. In terms of A, what is the area of △𝑆𝑇𝑈 in square inches?
Question
Suppose that △𝑃𝑄𝑅 has an area of A square inches and that the vertices of △𝑆𝑇𝑈 are the midpoints of the sides of △𝑃𝑄𝑅. In terms of A, what is the area of △𝑆𝑇𝑈 in square inches?
Solution
The area of a triangle is given by the formula 1/2 * base * height.
When the vertices of triangle STU are the midpoints of the sides of triangle PQR, triangle STU is similar to triangle PQR but its dimensions are half.
Therefore, the base and the height of triangle STU are each half of the base and the height of triangle PQR.
Substituting these into the area formula gives 1/2 * (1/2 base of PQR) * (1/2 height of PQR) = 1/2 * 1/4 * (base of PQR * height of PQR) = 1/4 * area of PQR.
So, the area of triangle STU is 1/4 of the area of triangle PQR.
If the area of triangle PQR is A square inches, then the area of triangle STU is A/4 square inches.
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