Question

find the area of the figure. hint: separate into regular shapes and combine the areas! a = ? cm² area formulas b×h (for the rectangular shape) and \\(\frac{b×h}{2}\\) (for the triangular shape). the figure has a green triangle (height 20 cm, base 20 cm) on top of a green square (side 20 cm).

Explanation:

Step1: Calculate area of square

The square has side length \( 20 \, \text{cm} \). Using the formula for the area of a square (or rectangle, here \( b = h = 20 \)) \( A_{\text{square}} = b \times h \).
\( A_{\text{square}} = 20 \times 20 = 400 \, \text{cm}^2 \)

Step2: Calculate area of triangle

The triangle has base \( b = 20 \, \text{cm} \) and height \( h = 20 \, \text{cm} \). Using the formula for the area of a triangle \( A_{\text{triangle}} = \frac{b \times h}{2} \).
\( A_{\text{triangle}} = \frac{20 \times 20}{2} = 200 \, \text{cm}^2 \)

Step3: Combine the areas

Add the area of the square and the area of the triangle to get the total area of the figure.
\( A_{\text{total}} = A_{\text{square}} + A_{\text{triangle}} = 400 + 200 = 600 \, \text{cm}^2 \)

Answer:

\( 600 \)