Question

workbook

1. for each picture, name the shape and calculate the area.

a)
b)
c)
d)
e)
f) what do you notice about the area calculations?

Explanation:

Step1: Identify the shape and formula for area

• a) The shape is 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). Here, \(l = 8.5\) m and \(w=5.2\) m.

$$A = 8.5\times5.2$$

$$A = 44.2\space m^{2}$$

• b) The shape is a parallelogram. The formula for the area of a parallelogram is \(A = b\times h\) (where \(b\) is the base and \(h\) is the height). Here, \(b = 8.5\) m and \(h = 5.2\) m.

$$A=8.5\times5.2$$

$$A = 44.2\space m^{2}$$

• c) The shape is a right - triangle. The formula for the area of a triangle is \(A=\frac{1}{2}\times b\times h\). Here, \(b = 8.5\) m and \(h = 5.2\) m.

$$A=\frac{1}{2}\times8.5\times5.2$$

$$A = 22.1\space m^{2}$$

• d) The shape is a triangle. Using the formula \(A=\frac{1}{2}\times b\times h\) with \(b = 8.5\) m and \(h = 5.2\) m.

$$A=\frac{1}{2}\times8.5\times5.2$$

$$A = 22.1\space m^{2}$$

• e) The shape is a triangle. Using the formula \(A=\frac{1}{2}\times b\times h\) with \(b = 8.5\) m and \(h = 5.2\) m.

$$A=\frac{1}{2}\times8.5\times5.2$$

$$A = 22.1\space m^{2}$$

Step2: Analyze part f)

For the rectangle and parallelogram, the areas are equal (\(44.2\space m^{2}\)) since the formula \(A = b\times h\) (where for the rectangle \(h\) is the width) is used. For the three triangles (c, d, e), the area formula \(A=\frac{1}{2}\times b\times h\) gives the same area (\(22.1\space m^{2}\)) because they have the same base (\(b = 8.5\) m) and height (\(h = 5.2\) m). The area of each triangle is half of the area of the rectangle (or parallelogram) with the same base and height.

Answer:

a) Rectangle, \(44.2\space m^{2}\)
b) Parallelogram, \(44.2\space m^{2}\)
c) Right - triangle, \(22.1\space m^{2}\)
d) Triangle, \(22.1\space m^{2}\)
e) Triangle, \(22.1\space m^{2}\)
f) The area of the rectangle and parallelogram (with same base and height) are equal. The area of each triangle (with the same base and height as the rectangle/parallelogram) is half of the area of the rectangle/parallelogram.