Area of composite figures (see also 5.4) Knowledge-Based Practice

Questions

1. 1.

   A composite figure consists of a central square with a side length of 6 cm and four congruent triangles, each having a base of 6 cm and a perpendicular height of 5 cm, attached to each side of the square. What is the total area of the composite figure?

   • A) 60 cm²
   • B) 96 cm²
   • C) 156 cm²
   • D) 51 cm²
2. 2.

   A composite figure is formed by joining a trapezoid and a triangle along a shared edge. The trapezoid has parallel bases of 15 cm and 9 cm with a perpendicular height of 6 cm, and the triangle shares the 15 cm base with a perpendicular height of 8 cm. What is the total area of the composite figure?

   • A) 105 cm²
   • B) 132 cm²
   • C) 168 cm²
   • D) 192 cm²
3. 3.

   A composite figure is formed by joining a rectangle measuring 9 cm by 4 cm and a parallelogram with a base of 9 cm and a perpendicular height of 5 cm along their common 9 cm side. What is the total area of the composite figure?

   • A) $58.5\text{ cm}^2$
   • B) $72\text{ cm}^2$
   • C) $90\text{ cm}^2$
   • D) $81\text{ cm}^2$
4. 4.

   A square piece of cardboard with a side length of 12 cm has a rectangular section measuring 5 cm by 4 cm removed from it. What is the area of the remaining cardboard?

   • A) 116 cm²
   • B) 124 cm²
   • C) 144 cm²
   • D) 164 cm²
5. 5.

   A composite figure is formed by attaching a right-angled triangle with a base of 8 cm and a height of 6 cm to the 6 cm side of a rectangle measuring 14 cm by 6 cm. What is the total area of the composite figure?

   • A) 96 cm²
   • B) 108 cm²
   • C) 120 cm²
   • D) 132 cm²

Answers and step-by-step solutions appear after you finish the test.