Find the areas of the figures below by dividing them into rectangles and triangles.

Question

Accepted Answer

Each figure is on a grid of unit squares. Cut it up with a few dashed lines, work out the pieces, and add.

Figure a — a parallelogram. Cut off the top and bottom triangles and leave a rectangle in the middle.

Figure a = triangle (2) + rectangle (4 × 5 = 20) + triangle (2).

Rectangle 4 × 5 = 20 Two triangles ½ × 4 × 1 = 2 each
Area = 20 + 2 + 2 = 24 square units

Figure b — a trapezium. Same idea: a rectangle in the middle with a triangle above and below.

Figure b = triangle (6) + rectangle (4 × 5 = 20) + triangle (4).

Triangle above = ½ × 4 × 3 = 6 Rectangle = 4 × 5 = 20 Triangle below = ½ × 4 × 2 = 4
Area = 6 + 20 + 4 = 30 square units

Figure c — the kite-like figure. Here it is easier to draw the smallest rectangle around it and subtract the four corner triangles.

Figure c sits inside a 6 × 12 rectangle. Subtract the four corner triangles: 3 + 3 + 15 + 3 = 24.

Surrounding rectangle = 6 × 12 = 72
Corner triangles = 3 + 3 + 15 + 3 = 24
Area = 72 − 24 = 48 square units

Figure d — the rectangle with a notch.

Figure d = a 4 × 5 rectangle with a triangular notch of area 4 cut out of the top.

Rectangle = 4 × 5 = 20 Notch = ½ × 4 × 2 = 4
Area = 20 − 4 = 16 square units

Figure e — the kite. Split it along the horizontal diagonal.

Figure e = upper triangle (4) + lower triangle (8).

Upper triangle = ½ × 4 × 2 = 4 Lower triangle = ½ × 4 × 4 = 8
Area = 4 + 8 = 12 square units

Figure	a	b	c	d	e
Area (sq units)	24	30	48	16	12

Two tools, use whichever is shorter: (i) add — cut the figure into rectangles and triangles; (ii) subtract — box the figure inside a rectangle and take away the corner triangles. Figures c and d are much quicker by subtraction.

NCERT Solutions Ganita Prakash Chapter 6 Areas by splitting into rectangles and triangles — Figure it Out