http://blog.nightlynexus.com/time-to-learn-the-very-basics-of-onmeasure/

SquareFrameLayout.java

/*
 * Copyright (C) 2016 Eric Cochran
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

import android.content.Context;
import android.util.AttributeSet;
import android.widget.FrameLayout;

import static android.view.View.MeasureSpec.EXACTLY;
import static android.view.View.MeasureSpec.UNSPECIFIED;

public class SquareFrameLayout extends FrameLayout {
  public SquareFrameLayout(Context context, AttributeSet attrs) {
    super(context, attrs);
  }

  @Override protected void onMeasure(int widthMeasureSpec, int heightMeasureSpec) {
    int widthMode = MeasureSpec.getMode(widthMeasureSpec);
    int heightMode = MeasureSpec.getMode(heightMeasureSpec);
    int widthSize = MeasureSpec.getSize(widthMeasureSpec);
    int heightSize = MeasureSpec.getSize(heightMeasureSpec);
    float widthToHeightRatio = 1f; // Is a square.
    int width;
    int height;
    if (widthMode == UNSPECIFIED && heightMode == UNSPECIFIED
        || widthMode != UNSPECIFIED && heightMode != UNSPECIFIED) {
      if (widthSize / widthToHeightRatio > heightSize) {
        // Limited by height.
        width = (int) (heightSize * widthToHeightRatio);
        height = heightSize;
      } else {
        // Limited by width.
        width = widthSize;
        height = (int) (widthSize / widthToHeightRatio);
      }
    } else if (widthMode == UNSPECIFIED) {
      // Limited by height.
      width = (int) (heightSize * widthToHeightRatio);
      height = heightSize;
    } else {
      // Limited by width.
      width = widthSize;
      height = (int) (widthSize / widthToHeightRatio);
    }
    super.onMeasure(MeasureSpec.makeMeasureSpec(width, EXACTLY),
        MeasureSpec.makeMeasureSpec(height, EXACTLY));
    if (widthMode == EXACTLY && heightMode == EXACTLY) {
      setMeasuredDimension(widthSize, heightSize);
    } else if (widthMode == EXACTLY) {
      setMeasuredDimension(widthSize, getMeasuredHeight());
    } else if (heightMode == EXACTLY) {
      setMeasuredDimension(getMeasuredWidth(), heightSize);
    }
  }
}