If a composite shape can be split into a rectangle and a triangle, the area is the sum of the areas of those shapes.

• A. True
• B. False
• C. Sometimes true only if shapes share a side
• D. Only if the triangle is right-angled

Answer: (A)

Think of a shape’s area as the amount of space it occupies. If you can cut the shape into pieces that don’t overlap and together fill the whole figure, the total area is the sum of the areas of those pieces. Here, the shape is split into a rectangle and a triangle. You find the rectangle’s area by multiplying its length by its width. You find the triangle’s area by one-half times its base times its height. Since these two pieces fit together exactly, you simply add those two areas to get the total area. This works whether the triangle is right-angled or not, as long as you use the appropriate base and corresponding height for that triangle and there are no gaps or overlaps.