GAT Geometry and Spatial 3

Question 1

A rectangle has a length of 12 cm and a width of 5 cm. What is the length of its diagonal?

Accepted Answer

13 cm

Answer

Using the Pythagorean theorem: diagonal = √(12² + 5²) = √(144 + 25) = √169 = 13 cm.

Question 2

What is the area of a circle with a diameter of 14 cm? (Use π ≈ 22/7)

Accepted Answer

154 cm²

Answer

Radius = 14/2 = 7 cm. Area = π × r² = (22/7) × 49 = 22 × 7 = 154 cm².

Question 3

A cube has a surface area of 150 cm². What is the length of one edge?

Accepted Answer

5 cm

Answer

A cube has 6 identical square faces. Area of one face = 150/6 = 25 cm². Edge length = √25 = 5 cm.

Question 4

If a shape is rotated 90° clockwise, which of the following is true about an arrow originally pointing upward?

Accepted Answer

It points right

Answer

A 90° clockwise rotation turns an upward-pointing arrow to point to the right.

Question 5

Two similar triangles have a scale factor of 3:5. If the area of the smaller triangle is 27 cm², what is the area of the larger triangle?

Accepted Answer

75 cm²

Answer

For similar figures, the ratio of areas equals the square of the scale factor. Area ratio = (3/5)² = 9/25. So 27/x = 9/25, giving x = 75 cm².

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