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JulijaS [17]
3 years ago
14

What is 1/3 of 21, 2/5 of 40 4/7 of 280

Mathematics
2 answers:
Lubov Fominskaja [6]3 years ago
7 0
\frac{1}{3} \times 21=\frac{21}{3}=\frac{7 \times 3}{3}=7 \\ \\
\frac{2}{5} \times 40=\frac{2 \times 40}{5}=\frac{2 \times 8 \times 5}{5}=2 \times 8=16 \\ \\
\frac{4}{7} \times 280=\frac{4 \times 280}{7}=\frac{4 \times 40 \times 7}{7}=4 \times 40=160
lana [24]3 years ago
5 0
A\ fraction\ of\ the\ number\ is\ equal\\to\ the\ product\ of\ the\ fraction\ by\ the\ number.\\\\Therefore:\\\\\frac{1}{3}\ of\ 21=\frac{1}{\not3_1}\cdot\not21^7=1\cdot7=\boxed7\\\\\frac{2}{5}\ of\ 40=\frac{2}{\not5_1}\cdot\not40^8=2\cdot8=\boxed{16}\\\\\frac{4}{7}\ of\ 280=\frac{4}{\not7_1}\cdot\not280^{40}=4\cdot40=\boxed{160}
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Answer:

Area = (18 + 4.5π) cm²

Perimeter = (6√2 + 12 + 3π) cm

Step-by-step explanation:

The shaded region given is made up of triangle ABC and a semicircle

AB = BC = 6 cm (note that the triangle is a portion of a square)

Diameter of semi-circle (d) = BC = 6cm

Radius (r) = ½*6 = 3 cm

==>Area of the shaded region in terms of π

Area of shaded region = area of triangle + area of semicircle

Area = ½*a*b + ½*πr²

Area = ½*6*6 + ½*π3²

Area = 18 + ½*π9

Area = 18 + 4.5π

<em>Area of the shaded portion = (18 + 4.5π) cm²</em>

==>Perimeter of shaded region in terms of π

Perimeter of shaded region = perimeter of triangle + perimeter of semicircle

= Sum of all sides of the triangle + ½πd

Sides of triangles are AB = 6 cm, BC = 6 cm

Use Pythagorean theorem to find side AC:

AC² = AB² + BC²

AC² = 6² + 6² = 36 + 36 = 72

AC = √72 cm

Perimeter of shaded triangle = √72 + 6 + 6 = √72 + 12 = (6√2 + 12) cm

Perimeter of semicircle = ½*πd = ½π6

= 3π

<em>Perimeter of the whole shaded region in terms of π = (6√2 + 12 + 3π) cm</em>

<em></em>

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3 years ago
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