Rectangle and Triangle

Part of the Polygons & Quadrilaterals section of Coddy's Geometry journey. Lesson 46 of 59.

A piece does not have to be a rectangle. A house shape is a rectangle with a triangle on top, and the dashed line between them is the cut. Each piece has its own rule.

$A house shape: a rectangle with a triangle roof, cut along DC; the roof height is 6$

Here the rectangle ABCD has sides 8 and 4, area 32. The roof triangle DCE has base DC = 8 and height EF = 6, so its area is $\frac{1}{2}\cdot 8\cdot 6 = 24$ . The whole shape: $32+24 = 56$ . The triangle's height is the dashed EF at right angles to DC, never a slanted side.

Challenge

The house shape ABCED is a rectangle ABCD with the roof DCE on top, cut along DC = 8. BC = 5 and the roof height EF = 3. Find the area of the whole shape, then press Check.

Try it yourself

$Find the marked part of the figure$