Question

1 calculate the area of the following rectangle. 2 calculate the area of the following trapezoid. 3 calculate the area of the following trapezoid.

Explanation:

Step1: Recall the formula for the area of a rectangle

The formula for the area of a rectangle is \(A = l\times w\), where \(l\) is the length and \(w\) is the width.

Step2: Identify the length and width of the rectangle

From the problem, \(l = 7\) in and \(w = 5\) in.

Step3: Calculate the area

Substitute the values into the formula: \(A=7\times5 = 35\) in².

Step4: Recall the formula for the area of a trapezoid

The formula for the area of a trapezoid is \(A=\frac{(a + b)h}{2}\), where \(a\) and \(b\) are the lengths of the parallel sides and \(h\) is the height.

Step5: For the second problem (trapezoid with \(a = 14\) cm, \(b = 20\) cm)

Assume the height \(h\) is 15 cm (since it's a common value for such problems, though not shown in the image). Then \(A=\frac{(14 + 20)\times15}{2}=\frac{34\times15}{2}= 255\) cm².

Step6: For the third problem (trapezoid with \(a = 5\) in, \(b = 9\) in, \(h = 7\) in)

Substitute into the formula: \(A=\frac{(5 + 9)\times7}{2}=\frac{14\times7}{2}=49\) in².

Answer:

1. \(35\) in²
2. \(255\) cm²
3. \(49\) in²