Question

Surely help me with this question

Answer 1

The area of the composite shape is:

• 122.50
  `cm^(2)`

Explanation:

To find the area of composite shapes you can pull apart this in known shapes, in this case, a rectangle and a triangle. Taking into account this, we can find the rectangle area firstly:

• Rectangle area = base * height

The base of the rectangle is the measure from down (14 cm) and the height is the measure in the left side (7 cm), with these values we can replace the formula:

• Rectangle area = base * height
• Rectangle area = 14 cm * 7 cm
• Rectangle area = 98
  `cm^(2)`

Now, to calculate the area of the remaining triangle, we must use the next formula:

• Triangle area =
  `(base*height)/(2)`

Where the base would be equal to the left side of the shape (7 cm) and the height is the difference between the measurement in the top side and the measurement in the bottom side:

• Height of the triangle = top side - bottom side
• Height of the triangle = 21 cm - 14 cm
• Height of the triangle = 7 cm

We can replace in the formula:

• Triangle area =
  `(7 cm * 7cm)/(2)`
• Triangle area =
  `(49cm^(2) )/(2)`
• Triangle area = 24.5
  `cm^(2)`

By last, we must add the two values of the areas obtained:

• Area of the composite shape = rectangle area + triangle area.
• Area of the composite shape = 98
  `cm^(2)` + 24.5
  `cm^(2)`
• Area of the composite shape = 122.5
  `cm^(2)`