Answer:
10) 474 units²
11) 28.3 cm² (nearest tenth)
Step-by-step explanation:
Question 10
To calculate the shaded area, subtract the area of the triangle from the area of the rectangle.
First, find the base of the triangle using Pythagoras' Theorem:
a² + b² = c²
(where a and b are the legs, and c is the hypotenuse of a right triangle)
Given:
Substituting the given values into the formula to find the base of the triangle:
⇒ a² + b² = c²
⇒ 16² + b² = 34²
⇒ b² = 34²- 16²
⇒ b² = 900
⇒ b = √(900)
⇒ b = 30
Area of triangle = 1/2 × base × height
= 1/2 × 30 × 16
= 240 units²
Area of rectangle = width × length
= 21 × 34
= 714 units²
Shaded area = area of rectangle - area of triangle
= 714 - 240
= 474 units²
Question 11
The central angle of the shaded area is a right angle = 90°
Angles around a point sum to 360°
[tex]\implies \sf \dfrac{90^{\circ}}{360^{\circ}}=\dfrac{1}{4}[/tex]
Therefore, the shaded area is a quarter of the area of the circle.
[tex]\begin{aligned}\textsf{Area of a circle} & = \sf \pi r^2 \quad \textsf{(where r is the radius)}\\\\\implies \textsf{Shaded Area} & = \sf \dfrac{1}{4}\pi r^2\\\\& = \sf \dfrac{1}{4}\pi (6)^2\\\\& = \sf 9\pi \:\:cm^2\\\\& = \sf 28.3\:\:cm^2\:\:(nearest\:tenth)\end{aligned}[/tex]
