12.a Angle 49° =

b. Angle 270° =
c. Circle with a radius of 3cm =
d. Line AB // CD 4cm a part and line EF# AB + CD =
e. Calculate the area , 12 cm , 7cm , 12cm , 7cm
f. Calculate the volume 4m , 4m , 4m
g. Calculate the area of the shaded if the triangle has 3m base 2m

Answer in number form

1 answer

Let's solve each part step by step:

a. Angle 49°

This is already in number form: 49°

b. Angle 270°

This is already in number form: 270°

c. Circle with a radius of 3 cm

The area \( A \) of a circle is calculated using the formula: \[ A = \pi r^2 \] Substituting the radius \( r = 3 \) cm: \[ A \approx 3.14 \times (3)^2 \approx 3.14 \times 9 \approx 28.26 , \text{cm}^2 \]

Answer: 28.26 cm²

d. Line AB // CD 4 cm apart and line EF # AB + CD

If line AB is parallel to line CD and they are 4 cm apart, we haven't been given sufficient information about EF. However, if the intention is to say that EF is also a line that runs between AB and CD or parallels them, no direct calculation can be made without additional information. Thus, we can't calculate a number here without assumptions.

Assuming a simpler interpretation, the distance between the lines is 4 cm.

Answer: 4 cm (for spacing between parallels)

e. Calculate the area of a 12 cm by 7 cm rectangle

The area \( A \) of a rectangle is calculated using the formula: \[ A = \text{length} \times \text{width} \] Substituting \( 12 , \text{cm} \) and \( 7 , \text{cm} \): \[ A = 12 \times 7 = 84 , \text{cm}^2 \]

Answer: 84 cm²

f. Calculate the volume of a cube with side lengths of 4 m

The volume \( V \) of a cube is calculated using the formula: \[ V = \text{side}^3 \] Substituting the side length \( 4 , \text{m} \): \[ V = 4^3 = 64 , \text{m}^3 \]

Answer: 64 m³

g. Calculate the area of the shaded region if the triangle has a base of 3 m and a height of 2 m

The area \( A \) of a triangle is calculated using the formula: \[ A = \frac{1}{2} \times \text{base} \times \text{height} \] Substituting the base and height: \[ A = \frac{1}{2} \times 3 \times 2 = \frac{6}{2} = 3 , \text{m}^2 \]

Answer: 3 m²

Summary of Answers

  • a. 49°
  • b. 270°
  • c. 28.26 cm²
  • d. 4 cm
  • e. 84 cm²
  • f. 64 m³
  • g. 3 m²