Find the area of the shaded region in the following figure.
Answers
Answer:
106cm²
Step-by-step explanation:
the side cm is 10 cm the other side is 6 cm and the cube represent 90cm so in total
10cm + 6cm+ 90 cm = 106cm
hope it will help you
Important Formulae
✽ Area of a rectangle: length × breath
✽ Area of a triangle: 1/2 × base × height
✽ Pythagoras theorem: the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the sides.
Answer
- Finding the area of rectangle PQRS
We know that:
⇒ Area of a rectangle = length x breath
⇒ Area of PQRS = 14 cm x 10 cm
= 140 cm²
- Finding TC
In order to find the area of ΔTCR, we need to know both the base (given) and the height (not given). As this is a right-angled triangle, we can find TC using the Pythagoras Theorem:
⇒ s² + s² = h²
⇒ RT² + TC² = CR²
⇒ 6² + TC² = 10²
⇒ TC² = 10² - 6²
⇒ TC² = 100 - 36
⇒ TC² = 64
⇒ TC = 8 cm
- Finding the area of ΔTCR
Here, base = TR = 6 cm
height = TC = 8 cm
We know that:
⇒ Area of a triangle = 1/2 × base × height
⇒ Area of TCR = 1/2 × 6 × 8
= 6 × 4
= 24 cm²
- Finding the area of the shaded portion
The area of the shaded portion is:
⇒ Area of rectangle - area of triangle
⇒ 140 cm - 24 cm
⇒ 116 cm²