Problem 1 :
Find the area of the figure ABCD shown below.
Problem 2 :
Find the height of a triangle that has an area of 12 square units and base length is 6 units.
Problem 3 :
A triangle has an area of 52 square feet and a base of 13 feet. Are all triangles with these dimensions congruent.
Problem 4 :
Find the area of trapezoid WXYZ shown below.
Problem 5 :
Find the area of the rhombus ABCD shown below.
Problem 6 :
Find the area of roof of the house shown below.
1. Answer :
Method 1 :
Use AB as the base. Then, b = 16 and h = 9.
Area of the figure ABCD is
= b ⋅ h
= 16 ⋅ 9
= 144 square units
Method 2 :
Use AD as the base. Then, b = 12 and h = 12.
Area of the figure ABCD is
= b ⋅ h
= 12 ⋅ 12
= 144 square units
Notice that we get the same area with either base.
2. Answer :
Because we want to find height of the triangle, we have to rewrite the area formula such that h is alone on one side of the equation.
Formula to find area of a triangle :
A = 1/2 ⋅ b ⋅ h
Multiply both sides by 2.
2A = b ⋅ h
Divide both sides by b.
2A/b = h
Given : A = 12 and b = 6.
Then, we have
(2 ⋅ 12)/6 = h
4 = h
So, the height of the triangle is 4 units.
3. Answer :
Because we want to find height of the triangle, we have to rewrite the area formula such that h is alone on one side of the equation.
Using formula from Problem 2, the height of the triangle is
h = (2 ⋅ 52)/13
h = 8 feet
There area many triangles with these dimensions. Some are shown below.
4. Answer :
The height of the trapezoid WXYZ above is
h = 5 - 1
h = 4 units
Find the lengths of the bases :
b_{1} = YZ b_{1} = 5 - 2 b_{1} = 3 units |
b_{2} = XW b_{2} = 8 - 1 b_{2} = 7 |
Formula to find area of a trapezoid :
A = 1/2 ⋅ h ⋅ (b_{1} + b_{2})
Substitute h = 4, b_{1} = 3 and b_{2} = 7.
A = 1/2 ⋅ 4 ⋅ (3 + 7)
A = 20
So, the area of trapezoid WXYZ is 20 square units.
5. Answer :
Let d_{1} and d_{2} represent lengths of the diagonals AC and BD respectively.
d_{1 }= AC = 20 + 20 = 40 units
d_{1 }= BD = 15 + 15 = 30 units
Formula to find area of a rhombus :
A = 1/2 ⋅ d_{1} ⋅ d_{2}
Substitute d_{1} = 40 and d_{2} = 30.
A = 1/2 ⋅ 30 ⋅ 40
A = 600
So, the area of rhombus ABCD is 600 square units.
6. Answer :
G, H and K are trapezoids and J is a triangle. The hidden back and left sides of the roof are the same as the front and right sides.
Area of J = 1/2 ⋅ 20 ⋅ 9 = 90 ft^{2}
Area of G = 1/2 ⋅ 15 ⋅ (20 + 30) = 375 ft^{2}
Area of H = 1/2 ⋅ 15 ⋅ (42 + 50) = 690 ft^{2}
Area of K = 1/2 ⋅ 12 ⋅ (30 + 42) = 432 ft^{2}
The roof has two congruent faces of each type.
So, the total area is
= 2(90 + 375 + 690 + 432)
= 2(1587)
= 3174
So, the total area of the roof is 3174 square feet.
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