Question

1. using the two shapes below, write the ratio of the trapezoid area to the triangle area:

Explanation:

Step1: Calculate trapezoid area

The formula for the area of a trapezoid is \(A=\frac{(a + b)h}{2}\), where \(a = 12\mathrm{cm}\), \(b=15\mathrm{cm}\), \(h = 6\mathrm{cm}\).

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Step2: Calculate triangle area

The formula for the area of a triangle is \(A=\frac{bh}{2}\), where \(b = 12\mathrm{cm}\), \(h = 8\mathrm{cm}\).

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Step3: Find the ratio

The ratio of the trapezoid area to the triangle area is \(\frac{A_{trapezoid}}{A_{triangle}}=\frac{81}{48}\). Simplify the ratio by dividing both numerator and denominator by 3. \(\frac{81\div3}{48\div3}=\frac{27}{16}\)

Answer:

\(\frac{27}{16}\)