Problem 1 :
Shown is a square garden with a triangular pond. Find the area of the garden that is grass.
Solution :
area of square = a^{2}
a = 6m
area of square = (6)^{2}
area of square = 36m^{2}
area of triangle = 1/2 × b × h
Base (b) = 4m
Height (h) = 3m
area of triangle = 1/2 × 4 × 3
= 12/2
= 6m^{2}
The area of the garden that is grass = 36 - 6
= 30m^{2}
So, the area of the garden that is grass is 30m^{2}.
Problem 2 :
Shown is a triangular brick wall with a rectangular window. Find the area of the wall that is brick.
Solution :
area of rectangle = l × w
Length = 1.5m
Width = 2m
area of rectangle = 1.5 × 2
area of rectangle = 3m^{2}
area of triangle = 1/2 × b × h
Base (b) = 6m
Height (h) = 7m
area of triangle = 1/2 × 6 × 7
= 42/2
area of triangle = 21m^{2}
area of the wall = area of triangle - area of rectangle
= 21m^{2} - 3m^{2}
area of the wall = 18m^{2}
Problem 3 :
Shown is a pattern that is made from a rectangle and a triangle. Find the area of the pattern.
Solution :
area of rectangle = l × w
Length = 5cm
Width = 8cm
area of rectangle = 5 × 8
area of rectangle = 40 cm^{2}
area of triangle = 1/2 × b × h
Base (b) = 5 cm
Height (h) = 6 m
area of triangle = 1/2 × 5 × 6
= 30/2
area of triangle = 15cm^{2}
area of the pattern = area of rectangle + area of triangle -
= 40 cm^{2} + 15 cm^{2}
area of the pattern = 55cm^{2}
Problem 4 :
Shown below is a wall. Calculate the area of the wall.
Solution :
Area of trapezoid = 1/2 (a + b) × h
= 1/2 (3 + 4) × 3
= 1/2 × 7 × 3
= 21/2
= 10.5
So, area of the wall is 10.5m^{2}.
Problem 5 :
Shown below is a logo made from a square and two triangles. Calculate the area of the logo.
Solution :
area of square = a^{2}
a = 8cm
area of square = (8)^{2}
area of square = 64cm^{2}
area of triangle = 1/2 × b × h
Base (b) = 8cm
Height (h) = 7cm
area of triangle = 1/2 × 8 × 7
= 56/2
= 28cm^{2}
area of triangle = 1/2 × b × h
Base (b) = 8cm
Height (h) = 7cm
area of triangle = 1/2 × 8 × 7
= 56/2
= 28cm^{2}
area of the logo = area of square + 2(area of rectangle)
= 64 + 2(28)
= 64 + 56
= 120
So, area of the logo is 120 cm^{2}.
Problem 6 :
Below is a diagram of a right-angled triangle and a square.
The area of the square is twice the area of the triangle.
Calculate the length of each side of the square.
Solution :
area of triangle = 1/2 × b × h
Base (b) = 16cm
Height (h) = 4cm
area of triangle = 1/2 × 16 × 4
= 64/2
area of triangle = 32cm^{2}
The area of the square is twice the area of the triangle.
So, area of the square is 2 × 32
= 64 cm^{2}
area of square = a^{2}
64 = a^{2}
a = √64
a = 8
So, the length of each side of the square is 8 cm.
Problem 7 :
The area of the triangle is 165cm^{2}, find b.
Solution :
area of triangle = 1/2 (b × h)
base = b
height = 15 cm
165 = 1/2 × b × 15
165 = 15/2 × b
(165 × 2)/15 = b
330/15 = b
b = 22
Problem 8 :
Shown below is a right-angled triangle.
The area of the triangle is 21cm^{2}. Calculate y, the length of the base.
Solution :
area of triangle = 1/2 (b × h)
base = y
height = 6 cm
21 = 1/2 × b × 6
21 = 6/2 × b
(21 × 2)/6 = b
42/6 = b
b = 7
Hence y the length of the base is 7 cm.
Problem 7 :
Below is a right-angled triangle and a rectangle.
The area of the right-angled triangle is equal to the area of the rectangle. calculate x.
Solution :
area of triangle = 1/2 × b × h
Base (b) = 5 cm
Height (h) = 12 cm
area of triangle = 1/2 × 5 × 12
= 60/2
= 30
area of rectangle = l × w
Length = 10 cm
Width = x cm
area of rectangle = 10 × x
Area of the right-angled triangle is equal to the area of the rectangle.
30 = 10x
x = 30/10
x = 3 cm
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM