Question : The sides of a triangle are 20 cm, 21 cm, and 29 cm. The area of the triangle formed by joining the midpoints of the sides of the triangle will be:
Option 1: $67 \frac{2}{3}$ cm2
Option 2: $52 \frac{1}{2}$ cm2
Option 3: $47 \frac{1}{2}$ cm2
Option 4: $58 \frac{1}{3}$ cm2
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Correct Answer: $52 \frac{1}{2}$ cm2
Solution : Given: The sides of a triangle = 29 cm, 21 cm, and 20 cm We can see, $29^2 = 21^2 + 20^2$ So, this is a right-angled triangle. ⇒ Area $=\frac{1}{2}\times 21\times 20=210$ cm2 Area of the smaller triangle $=\frac14\times210=\frac{105}{2}=52\frac12$ cm$^2$ Hence, the correct answer is $52\frac12$ cm$^2$.
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Question : Two triangles XYZ and UVW are congruent. If the area of $\triangle$XYZ is 58 cm2, then the area of $\triangle$UVW will be:
Option 1: 58 cm2
Option 2: 116 cm2
Option 3: 29 cm2
Option 4: 15 cm2
Question : The hypotenuse of a right-angled triangle is 39 cm and the difference of the other two sides is 21 cm. Then, the area of the triangle is:
Option 1: 270 cm2
Option 2: 450 cm2
Option 3: 540 cm2
Option 4: 180 cm2
Question : The sides of a triangle are of length 8 cm, 15 cm, and 17 cm. Find the area of the triangle.
Option 1: 65 cm2
Option 2: 75 cm2
Option 3: 60 cm2
Option 4: 70 cm2
Question : The sides of a triangle are 16 cm, 12 cm, and 20 cm. Find the area.
Option 1: 64 cm2
Option 2: 112 cm2
Option 3: 96 cm2
Option 4: 81 cm2
Question : In an isosceles triangle, if the unequal side is 8 cm and the equal sides are 5 cm, then the area of the triangle is:
Option 1: 12 cm2
Option 2: 25 cm2
Option 3: 6 cm2
Option 4: 11 cm2
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