Find the area of each of the following composite shape

Explanation

1. ACBD is a quadrilateral that can be split into two triangles: ΔABC and ΔABD.
   • Area ACBD = Area ΔABC + Area ΔABD
2. Write the formula for the area of a triangle containing base and height.
   • A_triangle = \(\frac12\) bh
3. Identify the values of b and h for ΔABC.
   • ΔABC: b = AB =8, h = EC = 6
4. Substitute the values of the pronumerals into the formula and, hence, calculate the area of ΔABC.
   • Area of ΔABC = \(\frac12\) ×AB×EC = \(\frac12\) ×8×6 = 24 cm²
5. Identify the values of b and h for ΔABD.
   • ΔABD: b=AB=8, h=FD=2
6. Calculate the area of ΔABD.
   • Area of ΔABD = \(\frac12\) AB×FD = \(\frac12\) × 8 × 2 = 8 cm²
7. Add the areas of the two triangles together to find the area of the quadrilateral ACBD.
   • Area of ACBD = 24 cm² +8 cm² = 32 cm²