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1 answer:
Answer:
Step-by-step explanation:
Area of square= l×l
Area of square= 6mm × 6mn
Area if square = 36 mm²
Area of triangle 1= ½b ×h
Area of triangle 1= ½ (6mm)(8mm)
Area of triangle 1 = 24 mm²
Area of triangle 2 is the same as area of traingle 1 because they have the same base and hight
: . area of triangles is 48mm²
Area of the figure= Area of square + Area of triangles
A of figure = 36+48
A of figure = 84 mm²
Option 2
Use trapezium formula
Area of trapezium= (a+b)/2 * h
a=6 mm (base)
b=8+6=14 mm (Base)
h= 6mm (height)
Therefore the area of triangle= 24mm² as calculated in option 1
Area of the figure= Area of trapezium +Area of triangle
Area of figure = 60+24
= 84 mm²
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Answer:
(i) see first attached diagram
(ii) QR = 22.67 km (2 dp)
(iii) 243°
Step-by-step explanation:
A bearing is the angle in degrees measured clockwise from north.
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<u>Part (i)</u>
see first attached diagram
<u>Part (ii)</u>
The angles marked in blue on the second attached diagram are Consecutive Interior Angles. In this case they add to 180° as the North lines are parallel.
The sum of angles around a point is 360°
⇒ m∠QPR (shown in red on the second attached diagram) = 360 - 150 - (180 - 15) = 45°
To calculate the distance between Q and R (marked in red on the attached diagram), use the cosine rule.
⇒ QR² = PR² + QP² - 2(PR)(QP)cos(QPR)
⇒ QR² = 32² + 24² - 2(32)(24)cos(45)
⇒ QR² = 513.8839841...
⇒ QR = √513.8839841...
⇒ QR = 22.67 km (2 dp)
<u>Part (iii)</u>
We need to find the angle marked in green on the third attached diagram.
To do this, we need to find the angle marked in pink and the angle marked in orange, then subtract them from 360°
Pink angle = 180 - 150 = 30° (using the same consecutive angle theorem as before)
Orange angle (o) using the sine rule:
⇒ sin(o)/32 = sin(45)/QR
⇒ sin(o) = 32sin(45)/22.67
⇒ sin(o) = 0.9981652337...
⇒ o = 86.52868176...°
Therefore, the green angle = 360 - 30 - 86.52868176... = 243° (nearest degree)
