Decompose to Rectangles
Find the area of a 6 m by 4 m rectangle.
24 m2
Find the area of a triangle with base 8 cm and height 5 cm.
Area = 1/2 × 8 × 5 = 20
Find the area of a rectangle with length 2.5 m and width 1.2 m. (Multiply decimals)
2.5×1.2=3.0 m2
A garden is a rectangle 10 ft long and 4 ft wide. How many square feet of sod are needed?
40 ft2
A regular rectangle is cut into 2 triangles. If the rectangle area is 48 cm2, what is the area of one triangle?
48 ÷ 2 = 24 cm2
A 6 by 8 L-shaped figure is made by joining two rectangles: one 6 by 3 and one 6 by 5. Find the total area.
6×3 + 6×5 = 18 + 30 = 48
A right triangle has legs 6 cm and 8 cm. Find its area by treating it as half of a rectangle.
Area = 1/2 × 6 × 8 = 24
A triangle has base 3/4 ft and height 2/3 ft. Find its area. (Work with fractions)
Area = 1/2×3/4×2/3=1/4 ft2
A triangular sail has base 8 ft and height 6 ft. How much fabric (in square feet) is needed to make the sail?
1/2 x 8 x 6 = 24 ft2
A pentagon can be split into a rectangle (area 20) and a triangle (area 12). Find the pentagon's area.
20 + 12 = 32
A trapezoid can be decomposed into a rectangle and a triangle. The trapezoid has bases 10 cm and 6 cm and height 4 cm. Decompose and find its area.
Area trapezoid = average base × height =
((10+6)/2)×4 = 32
An isosceles triangle has base 10 cm and total area 30 cm2. Find the height.
Height = (2×Area)/base = (2×30)/10 = 6
A rectangle measures 4.25 cm by 3.6 cm. Find the area and round to the nearest hundredth.
4.25×3.6=15.3 cm2
A rectangular poster 24 in by 18 in has a decorative triangular corner removed with base 6 in and height 4 in. How much area remains for text?
Poster area 24×18 = 432; removed triangle = 1/2×6×4 = 12; remaining = 420 in2
A polygon is decomposed into three triangles with areas 8, 10, and 12 square units. What is the polygon's area?
8 + 10 + 12 = 30
Decompose the following irregular polygon into rectangles: a shape made of a 7 cm by 4 cm rectangle attached to a 3 cm by 4 cm rectangle along the 4-cm side. What is the area?
7×4 + 3×4 = 28 + 12 = 40
A triangle has vertices that make a rectangle of 12 cm by 5 cm when completed; the triangle uses half of that rectangle. Find the triangle's area.
Rectangle area = 12×5 = 60, triangle = half → 30
A parallelogram has base 5225 m and height 1.61.6 m. Find its area.
Area = 5/2×1.6=4.0 m2
A rectangular room is 12.5 ft by 9.75 ft. Find the floor area in square feet.
12.5×9.75=121.875 ft2
A trapezoid is decomposed into a rectangle of width 6 and height 4, and two congruent right triangles on the sides. Each triangle has base 2 and height 4. Find the trapezoid's area.
Rectangle = 6×4 = 24;
triangles = 2×(1/2×2×4)=2×4=8;
total = 32
A composite figure consists of a 9 in by 4 in rectangle with a 3 in by 3 in square removed from one corner. Find the remaining area.
9×4 − 3×3 = 36 − 9 = 27
A triangle's base is 7.5 m and its area is 33.75 m2. Find the height.
Height = (2×33.75)/7.5 = 9
A composite figure contains a rectangle 3 1/2 in by 2.25 in and a right triangle with base 1 1/2 in and height 2.25 in attached along the long side. Find the total area.
Rectangle: 3.5×2.25=7.875; Triangle: 1/2×1.5×2.25=1.6875; Total = 9.5625 in2
A flower bed is a regular hexagon decomposed into 6 equilateral triangles each with area 7.5 m2. What is the total area of the flower bed?
6×7.5 = 45 m2
A regular octagon can be decomposed into a central rectangle and 4 congruent isosceles triangles. If each triangle has area 6 and the rectangle's area is 24, what is the octagon's area?
4 triangles total area = 4×6 = 24; plus rectangle 24 → total 48