Question

find the area of the figure. hint: separate into regular shapes and combine the areas! a = ? cm² area formulas: rectangle (b×h), triangle ((\frac{b \times h}{2})). the figure has a triangle with base segments 16 cm, 16 cm (total base 32 cm), height 20 cm; and a rectangle with width 16 cm, height 20 cm.

Explanation:

Step1: Identify the two shapes (triangle and rectangle)

The figure consists of a triangle (top) and a rectangle (bottom). For the triangle, base \( b = 16 + 16 = 32 \) cm, height \( h = 20 \) cm. For the rectangle, length \( l = 16 \) cm, height \( h = 20 \) cm.

Step2: Calculate area of triangle

Using triangle area formula \( A_{\text{triangle}} = \frac{b \times h}{2} \), substitute \( b = 32 \), \( h = 20 \):
\( A_{\text{triangle}} = \frac{32 \times 20}{2} = 320 \) \( \text{cm}^2 \).

Step3: Calculate area of rectangle

Using rectangle area formula \( A_{\text{rectangle}} = l \times h \), substitute \( l = 16 \), \( h = 20 \):
\( A_{\text{rectangle}} = 16 \times 20 = 320 \) \( \text{cm}^2 \).

Step4: Sum the areas

Total area \( A = A_{\text{triangle}} + A_{\text{rectangle}} = 320 + 320 = 640 \) \( \text{cm}^2 \).

Answer:

640