Two shapes overlap
Primary 5 overlapping shapes area questions: add the two identical shapes, subtract the shared part once, and work back to an overlap or a side.
Questions in this lesson
- 0:05 Today's question: Two identical squares of side 10 cm overlap. The part where they overlap is a square of…
- 1:09 Example 1: Two identical right-angled triangles overlap. Each triangle has a base of 16 cm. Its…
- 2:16 Example 2: Triangles ABC and STU are identical right-angled triangles that overlap. Each triangle…
Transcript
Two identical squares of side 10 centimetres overlap. The part where they overlap is a square of side 4 centimetres. Find the area of the figure the two squares cover. Look at the piece the two squares share. Area covered is both shapes minus one shared part. One square is 10 centimetres times 10 centimetres. Its area is one hundred square centimetres. The shared square is 4 centimetres times 4 centimetres. Its area is 16 square centimetres. Now look at the area covered. It is one hundred square centimetres plus one hundred square centimetres. The shared piece is in there twice. The paper has that piece once. So minus one shared part. One hundred plus one hundred minus 16 is one hundred and eighty four square centimetres.
Now work the same idea backwards. Two identical right-angled triangles overlap. Each triangle has a base of 16 centimetres. Its height is 12 centimetres. Together they cover an area of one hundred and fifty square centimetres. Find the area of the part where the two triangles overlap. The question asks for the shared part. The overlap is the two triangles minus the area covered. Area of one triangle is half of 16 centimetres times 12 centimetres. Cross out the 2 under the line, and the 16 becomes 8. 8 times 12 is 96 square centimetres. Two triangles have an area of one hundred and ninety two square centimetres. The figure covers one hundred and fifty square centimetres. One hundred and ninety two minus one hundred and fifty is 42. The overlap is 42 square centimetres.
Your turn. In the figure, triangles A B C and S T U are identical right-angled triangles that overlap. Each triangle has a base of 20 centimetres. Its height is 8 centimetres. The two shaded parts are outside the overlap. Their total area is one hundred square centimetres. Find the area of the unshaded part where the two triangles overlap. Try it first. Pause if you like. The two triangles are identical. Take out the overlap from the first triangle. One shaded piece is left. Take out the same overlap from the second triangle. The other shaded piece is left. Put the two triangles side by side. Each one loses the same shared part. So the two shaded pieces are equal. Area of one triangle is half of 20 centimetres times 8 centimetres. Cross out the 2 under the line, and the 20 becomes 10. 10 times 8 is 80 square centimetres. The two shaded pieces total one hundred square centimetres. One shaded piece is 50 square centimetres. 80 minus 50 is 30. The overlap is 30 square centimetres. A shared piece is inside both shapes. On the sheet, a shared piece is there once. In the sum, a shared piece is there twice. The difference between them is one shared part.